Jimmy Carter can win the 1980 presidential election if positive economic trends continue and just a tiny percentage of voters now leaning toward one of his opponents decides that the president deserves some of the credit.

But if Carter fails to get any credit for what many voters currently perceive to be an improving economy, a November victory for Ronald Reagan appears likely.

These are among the chief findings of a new Washington Post poll that shows Carter and Reagan tied in the popular vote, with each drawing support from 37 percent of registered voters. Independent candidate John B. Anderson is far behind at 13 percent.

Much of Carter's strength comes from a breakthrough in the South, where he leads Reagan by 47 to 34 percent. He still trails Reagan in the other regions and would seem to be a sure loser in the electoral vote if the election were held today.

Nevertheless, Carter is in a far better position than he was just before the Democratic convention, when some polls showed him behind his Republican opponent by as much as 25 to 30 points nationwide. Today, the ingredients for a Carter victory at least seem to be present, and the key ingredient could be shifting perceptions of the economy.

More and more voters appear to be gaining confidence in the economy, or at least expressing the conviction that things are no longer getting any worse. In a Washington Post poll last April, 47 percent of those interviewed said they thought they would be worse off financially in a year's time. In the new poll, only 27 percent felt they would be worse off a year from now.

In the April poll, Reagan had a 16-point margin over Carter as the candidate more likely to restore the value of the dollar. In the new poll, that margin stands at 11 percent, despite constant hammering away by Reagan on the issue of the economy.

Many political scientists have long maintained that presidential elections are determined by the incumbent's popularity and perceptions of the economy at the time of the election. The Post's poll helps explain why they hold that view.

Among the voters who think that the economy has stopped deteriorating and that Carter's record in office is at least passable, the president holds a huge 61-to-14 lead over Reagan, with Anderson at 9 percent.

The problem for Carter is that only 40 percent of the public believes both propositions. Despite the increasing optimism over the economy, Carter stands at as low a point in popularity as he ever has in a Post poll. On a scale of zero to 10, with zero representing the most unfavorable rating and 10 the most favorable, the president is given an overall score of 5.0.

When asked whether they feel Carter is "a better president than he is getting credit for" or whether he "just can't cut it as president," 47 percent choose the first statement and 44 percent say that he "can't cut it." That question has been asked several times in previous Post polls, and Carter has never been dealt such a poor score.

A total of 27 percent of the electorate believes that Carter's presidency has been a failure, but that the economy, at long last, has turned a corner. Among that group, Carter now loses to Reagan by an overwhelming 65 to 5, with Anderson at 14 percent.

It is among such voters that Carter must make inroads, and there are reasons to believe he can. Many of them are Democrats or people who say they are independents who lean Democrat. Many consider themselves liberals. In fact, many of these voters give every appearance of having been supporters of Sen. Edward M. Kennedy (D-Mass.), and their eventual vote could possibly be determined by the signals issued by Kennedy during the rest of the presidential campaign.

Carter has rebounded many times in the past and there is nothing in the poll to indicate that he can't do so once more between now and Nov. 4. Indeed, there are suggestions that the door is wide open.

Thirteen percent of the registered voters interviewed said they had made no choice yet, and an additional 19 percent said they did not feel strongly at all about the candidate they are currently backing. Anderson backers, a great many of them Democrats, were the most likely to say they had only loose ties to their candidate.

The poll was conducted by telephone from Sept. 3 to 7. A total of 2,314 people were interviewed, including 1,755 who said they were registered to vote. Most of the findings were taken from interviews with those who said they were registered.

The poll also found the existence of widespread discontent with Reagan. Asked whether they thought Reagan "is well qualified to be a good president or not," 43 percent said they thought he was and 41 percent said they thought he was not, with 16 percent saying they were not sure.

Nevertheless, the oft-repeated theme that both Carter and Reagan are unacceptable to a majority of voters -- a key element in the Anderson campaign -- appears to have been vastly overstated, to say the least.

According to the poll, only 12 percent of registered voters take extremely critical views of both Carter and Reagan at the same time. The majority may be down on one, but not the other. That 12 percent, as might be expected, forms the core of Anderson's support, accounting for more than one-third of those who say they are backing the Illinois congressman.

The poll delved into people's attitudes on a wide array of domestic and foreign policy issues, and toward perceptions of the candidates as well. It found voters to be as divided on many issues as they were on which candidate to vote for.

Carter was seen as having a better understanding than Reagan of "the problems of people like you" by 46 to 34, and was trusted more "to do the right thing" by 45 to 37 percent.Reagan was considered "more likely to get things done as president" than Carter by 44 to 35, as well as more able to restore the value of the dollar.

Carter was given a 42-to-35 edge as probably being "more effective in dealing with Congress," and was considered by 42 to 39 as being "better able to deal with hostile foreign governments."

By 44 to 26, Reagan was considered less likely to secure the release of the Americans being held hostage in Iran without resorting to military action. But, consistent with past polls, a plurality favored military action in Iran even if it jeopardizes the lives of the hostages -- and, by a narrow 43 to 40, those interviewed said they would rather see Reagan than Carter "in charge of handling our relations with Iran."

The conventional wisdom this year states that Carter has no "natural constituency" outside the South. The Post's poll, however, suggests that the president does have a sort of constituency that could prove vital: More voters are likely to side with his position and not Reagan's on a number of key issues.

One such issue is whether the United States should strive for military superiority over the Soviet Union or settle for military equality with that superpower. Carter has come down hard on the side of equality, charging that to seek superiority means getting into an unlimited arms race. Reagan has maintained that the United States must have superiority to assure the nation a "margin of safety."

The differences between the two candidates on the matter couldn't be greater. In the Post poll, 40 percent said they preferred superiority, and 48 percent said equality.

Another such issue has to do with government spending programs and taxes. Carter has pledged to begin a national health program, while Reagan has pledged that there will be no such program if he is president. In the poll, 56 percent said they favored a government-sponsored health care program, and 35 percent were opposed.

Reagan has made a massive tax-cutting plan the centerpiece of his economic proposals, and has stated that he will start no new government programs except for military ones. Carter has been more equivocal about tax cuts -- and the public overall tends to side more with the Carter position. Asked whether they agreed or disagreed with the statement that "the government ought to cut taxes right away, even if it means putting off some important things that need to be done," 39 percent agreed and 51 percent disagreed.

Of the three major candidates, only Anderson has come out in opposition to any tax cut.

The poll also found Carter leading Reagan among blacks nationwide by 73 to 9, with Anderson drawing 9 percent. Among whites, Reagan leads by 41 to 32 over Carter, with Anderson at 14 percent.

In addition, as has been noted in other recent polls, there appears to be sharp differences in the way men and women appraise the two major candidates. The Post poll shows Reagan leading among men nationwide by 43 to 33 -- but Carter ahead among women by the same percentages.

There was no way of telling from The Post's poll whether Reagan was hurt or Carter helped among women by their positions on the Equal Rights Amendment. Reagan is opposed to ratification of the amendment and Carter is a strong supporter.

One leading Republican pollster, Robert Teeter, said he felt Reagan's position on ERA had little to do with the finding, but rather that Reagan's overall positions seemed to appeal more to men than to women.