President Carter extended the embargo on grain shipments to the Soviet Union today, and President-elect Ronald Reagan indicated that he has not decided whether he will cancel the embargo as he promised during the presidential campaign.

Reagan won farmers' applause with campaign attacks on the embargo, but he said here today that ending the embargo "is something for a great deal of study."

"You have to determine whether we're having as much effect on the Soviet Union or if that's being offset by a worse effect on our own agricultural community," Reagan said.

Although Reagan's aides had indicated since the election that Reagan was having second thoughts about the embargo, this was the first time since he won the presidency that Reagan has discussed the issue.

The Carter administration has argued that the embargo, which covers grain, phosphates for fertilizer, oil and gas equipment and parts for the Soviet Kama River truck plant, is hurting the Soviets and that it continues to be justified by the Soviet presence in Afghanistan.

Carter imposed the embargo in response to the Soviet invasion of Afghanistan, and Commerce Secretary Philip M. Klutznick, in announcing the one-year extension, again cited the Soviet occupation of that country.

If Carter had not ordered the extension, some parts of the embargo would have expired at midnight Wednesday.

The grain embargo is unpopular with farmers who accuse the Carter administration of making them pay an economic price with a measure that is not seriously injuring its target -- the Soviet Union.

Throughout the presidential campaign, the Carter administration attempted, with little apparent success, to convince farmers that the embargo was working and that it was not damaging their efforts to sell their crops.

The Carter administration helped to open new export markets, and farm exports reached record highs last year, but farmers countered that the totals would have been even higher wihout the embargo.

In a brief exchange with reporters at Palm Springs Airport, Reagan also said he has not decided whether to reduce cost-of-living increases in Social Security and other federal benefits as part of his program to balance the budget.

"I think we're looking at everything," Reagan said. He added that he won't know whether benefits will be cut until he has had time to study all the reports that have been prepared by his task forces.

He took a swipe a the Carter administration's economic record by noting that, "We have discovered that the [budget] deficit is going to be double, what it had been estimated. The budget is going to be much bigger than they've been talking about all these past several months of the campaign."

Reagan said he would try to deal with that problem "without penalizing anyone who is dependent for help on the rest of us."

Reagan was asked what else he could trim from the federal budget. As he did often during the campaign, he pointed to the elimination of waste and fraud as a potential way to save money without causing pain to any group of citizens.

"I think there's a great deal of waste and fraud and so forth going on in government that's going to make for some savings, and we're going to look at every program," he said.

The president-elect and Mrs. Reagan flew to Los Angeles after spending a two-day New Year's holiday here as guests of publisher Walter Annenberg.

Reagan plans a quiet weekend at his Los Angeles home before flying to Juarez Monday for a meeting with Mexican President Jose Lopez Portillo.

Monday evening Reagan is scheduled to arrive in Washington for his third post-election visit to the capital.

He is to hold a series of meetings at Blair House with his top aides and some of his newly named Cabinet members before returning to Los Angeles Thursday.