Douglas Fraser, president of the United Auto Workers, launched a nationwide petition drive yesterday designed to stir up broad support among rank-and-file workers and the unemployed for a law requiring that cars sold in America be built largely in America.

This drastic approach to trade, known as the "content" bill, is the UAW's top priority on Capitol Hill, and has attracted unexpected support among members. It would require that the "content" of cars sold in America include from 25 percent to as much as 90 percent U.S. or Canadian parts and labor by 1985.

The Reagan administration, foreign car makers and other opponents, dismissing it as protectionism, gave the measure little chance of getting anywhere when it was introduced last December.

But as sales of U.S. autos fell to the lowest level in 20 years, unemployment soared and imports prospered, the political appeal brightened. The bill has 218 cosponsors in the House, 16 in the Senate.

"I think more and more members of Congress with long records as 'free traders' are realizing that this slogan of 'free trade,' particularly as practiced with the Japanese, has to be coupled with a demand for 'fair trade,' " Fraser told reporters at National Airport after he flew in from Detroit. He was en route to appointments with Rep. John D. Dingell (D-Mich.), chairman of the House Commerce Committee, and other key congressional leaders.

Because of the gigantic ripple effect the auto industry sends through the U.S. economy, 868,000 additional jobs would be gained for American workers by 1985 if the bill is enacted, Fraser contended. Much of organized labor is supporting the initiative, except for dockworkers and others who would be hurt by curtailment of imports.

To questions about the possibility of retaliation, Fraser responded that other countries already have content laws and do not suffer retaliation.

"I don't think Congress should be intimidated on this," he said. "They should worry about this country's industrial base."

The administration contends that the bill would raise auto prices, yield fewer jobs than the UAW expects, and violate free-trade agreements.

Fraser and others argue that the United States is playing by outmoded rules that other countries have abandoned with impunity.

The United States has been playing a "sucker" role in foreign trade, according to Rep. Richard L. Ottinger (D-N.Y.), who introduced the bill.

The content requirements would be phased in over three years and would hit those with the highest U.S. sales the hardest--Toyota and other Japanese makers. For instance, both foreign and domestic auto makers with sales of more than 500,000 would be required to have 90 percent domestic content in their cars for the 1985 model year. The percentage would decline on a sliding scale for those with lower sales.

Among others affected would be U.S. companies that have begun to import parts from other countries. Some foreign producers, such as Volkswagen, already make cars here, Fraser noted.

The drive to collect signatures on petitions is under way in unemployment lines and shopping centers in major cities, union officials said. This is part of a high-intensity lobbying effort designed to take full advantage of political vulnerabilities before the November elections.

According to a source from Dingell's committee, the bill must wait in line behind a heavy schedule of other important legislation.

As Fraser arrived, union foot soldiers looking for petition signatures worked the airport crowds around him. They wore UAW hats emblazoned "Buy American" and placards that said, "Build U.S. Jobs Part By Part."