Republican National Chairman Richard Richards yesterday predicted that the 1980s will see the GOP replace the Democrats as the majority party, chiefly because of President Reagan's popularity.

As evidence, he cited a new national survey by Richard Wirthlin, Reagan's campaign pollster, indicating that, for the first time in 44 years, the GOP has as good a public image as the Democratic Party has.

The poll found that 39 percent of Americans consider themselves Republicans, 40 percent consider themselves Democrats and 21 percent are independent. This is a dramatic change from a Wirthlin poll a year ago in which 30 percent considered themselves Republicans and 50 percent said they were Democrats.

(A Washington Post-ABC News poll in March reported sharp gains for Republicans, but the most recent Post-ABC poll, conducted in May, showed 51 percent of the respondents as Democrats, 36 percent as Republicans and 13 percent independent.)

"We're on the threshold of majority status," Richards said in a speech at the National Press Club, in which he predicted that Republicans will win control of the House in 1982, something that last occurred 30 years ago.

Democrats outnumber Republicans in the House, 243 to 192. Richards predicted that the GOP will pick up 12 to 15 seats through reapportionment, and that some conservative Democrats will switch to the GOP because "the Democratic Party has left many of its members."

Contrary to reports from the White House, he said the Republican National Committee and GOP congressional campaign committees have not agreed to give "a free ride" to conservative Democrats who support Reagan's budget and tax-cut proposals. However, he said it may be difficult to campaign against these Democrats on economic issues on which they agree with the president.

Richards also disputed claims by Democratic National Chairman Charles T. Manatt that Republicans won in 1980 because they had more advanced computer systems and were better organized. "We won because the American people believed we were right on the issues." Richards said.

He claimed that Republicans have become the party "of the little people." As evidence, he said the GOP has 1.2 million financial contributors, 70 percent of whom donate $25 or less.

The Republican National Committee meets later this week for the first time since Reagan's inauguration and it can expect similar upbeat messages from Richards.

"I look at the future of the Republican Party as better than any time in my lifetime," he said. "And the reason is Ronald Reagan.This is a man of destiny."