In a startling departure from orthodox campaigning, Geraldine A. Ferraro today bluntly challenged workers at the Chrysler Corp. automobile plant here to explain "why one-third of you are going to vote for Ronald Reagan."

"What I'm here for is not to learn how to torque a car, not for the photo opportunity," the Democratic vice-presidential nominee said. "We're running a campaign, and five weeks from today you're going to make a decision on who's going to run the country. I want to know why, why one-third of you are going to vote for Ronald Reagan."

Ferraro said she was "absolutely floored" by a poll showing strong support for the Republican ticket among the traditionally Democratic United Auto Workers, and she pleaded for "someone, anyone" to "let me know what the feelings are."

Slowly, hesitantly, some of the 200 workers told her. "We blame Jimmy Carter for a lot of the problems," one worker admitted. "Iran, weak foreign policy," another added.

"What Reagan has done, he's said the things the working man believes," another worker suggested. "I think the average working man is against the welfare system the way it's run now."

Point by point, Ferraro rebutted, cajoled, challenged.

"Remember, 52 hostages were in the embassy in Tehran . Fifty-two hostages came home alive. . . . Have those people who are still worrying about Iran seen what's happened in Beirut recently? Three bombings."

On the welfare system, Ferraro said, "What Reagan has done, very successfully, is say that we must cut programs in which there's waste -- like food stamps. We have a budget that's over $900 billion. You know how big the food stamp program is? Eleven billion dollars. You could eliminate the whole program and you wouldn't even do anything about budget deficits.

"There may be some cheating," she added, "but it doesn't hold a candle to the waste and cheating that's going on in the Defense Department."

Ferraro personally suggested the unusual strategy at the auto plant, according to campaign manager John Sasso, who added, "We talked about it afterwards and we think some of the real stuff bubbled up. We think it got to the real nub of why some working people are attracted to Ronald Reagan."

The workers appeared to listen attentively and applauded enthusiastically, particularly when Ferraro asked, "Are we standing tall in Lebanon with a president who doesn't take responsibility for what's happened? . . . That's not leadership."

Before leaving, Ferraro reminded the workers that she and Mondale had both supported the federal government's bailout of Chrysler in 1979.

"You don't turn your back on people who've been good to you and people who are looking to the future," she said.

Later, during a speech at Vanderbilt University in Nashville, Ferraro returned to the theme of presidential leadership as she attacked President Reagan for being an "anecdotal," "off-the-cuff," "eleventh-hour," "pass-the-buck" chief executive.

"This administration blames Congress for its budget deficit, Walter Mondale for its arms-control gridlock, and previous presidents for Beirut. As you say here in Tennessee, 'Mr. President, that dog don't hunt,' " Ferraro said.

Contrasting Reagan's record with that of her running mate, Walter F. Mondale, Ferraro said, "On arms control, Fritz Mondale has been out front. Name the last time President Reagan took the lead on an issue in advance of his time."