The United States and Canada have decided on a new "joint effort" to examine acid rain, sidestepping a politically sensitive dispute at the summit this weekend between President Reagan and Prime Minister Brian Mulroney, administration sources said yesterday.

The two leaders are expected to announce agreement on the effort after meeting Sunday and Monday in Quebec City, and will ask for a report on the results when they are next scheduled to meet a year from now, the sources said.

Their approach is a compromise designed both to help Mulroney, who has launched a major acid-rain cleanup effort, and to maintain Reagan's position that more research is needed before a costly U.S. cleanup program can be justified, the sources said.

There was a heated internal dispute in the Reagan administration before it was decided to go along with the "joint effort" at the weekend summit, officials said.

Acid rain is caused by the emission of sulfur dioxide, nitrogen oxide and traces of such toxic metals as mercury and cadmium from factories, power plants, autos and natural sources in the United States and Canada. The emissions mix with water vapor to produce weak solutions of nitric and sulfuric acids that then fall to earth and are believed to be causing damage to lakes and forests in the northeastern United States and Canada.

Last week, Mulroney's environment minister, Suzanne Blais-Grenier, announced a major acid-rain cleanup plan designed to reduce sulfur dioxide emissions by 50 percent in eastern Canada over the next nine years. The plan includes government financial aid to the smelting industry for pollution control, and stricter auto emission standards, among other measures.

But the Canadian plan also stressed that help from the United States is required for a "total solution to the acid-rain problem."

Reagan has resisted Canadian demands for more action on acid rain. Instead, the administration has said more study is necessary, and it has proposed increased funding for research into the causes and extent of the acid-rain problem.

A senior Canadian official told reporters last week, "In order to clean up Canada we need the cooperation of the United States because close to half the emissions that fall on Canada are originated here in the United States." The official said "we would hope that the stalemate, so to speak, could be broken in terms of a cooperative approach" at the summit.

But U.S. industry and Congress are sharply divided along regional lines over how to deal with acid rain, and particularly who should pay for what could be an expensive cleanup effort.

Opposition from David A. Stockman, director of the Office of Management and Budget, has stymied any more ambitious effort by the Reagan administration to clean up acid rain. In a written response to questions from the Canadian magazine Macleans released this week, Reagan recounted past U.S. efforts to clean up air pollution, and said:

"For the future, I believe it is a question of doing what is reasonable and responsible, after getting all the facts."

But officials said two key Reagan aides were responsible for getting the administration to make at least a token gesture to Mulroney on the issue: White House deputy chief of staff Michael K. Deaver, who is leaving in May to open his own consulting firm, and Richard R. Burt, assistant secretary of state for European and Canadian affairs.

Administration officials said Burt argued that Reagan should not give a cold shoulder to Mulroney on the acid-rain issue because of the importance of winning Canada's continuing support for U.S. arms control and foreign policy initiatives.