President-elect Ronald Reagan visited the headquarters of the International Brotherhood of Teamsters yesterday to thank the union personally for supporting his candidacy and to renew his campaign promise to put unemployed Americans back to work.

For the 2.3-million-member union, the nation's largest, the 20-minute visit was almost as important as the pledge. It marked the union's return to the political fast lane, from which it had been absent since the resignation of President Nixon in 1974.

The Teamsters union was the most notable labor organization to break away from the Democrats in 1972 to endorse Nixon. The union endorsed Jimmy Carter in 1976, but again broke ranks this year to go with Republican Reagan.

Yesterday in their well-appointed headquarters near the Capitol grounds, Teamsters officials and staffers were filled with obvious glee at having again chosen the right horse in the presidential race. Perhaps the proudest was their president, Frnak E. Fitzsimmons, who ushered Reagan and Vice President-elect George Bush into a private noon meeting with the union's general executive board.

"Fitz is just tickled that Reagan came here," said Teamsters spokesman Duke Zeller. However, Zeller denied that Fitzsimmons' delight was increased by Reagan's decision not to drop in on the headquarters of the AFL-CIO, a few miles away. The AFL-CIO had backed Carter.

Zeller said "no issues were raised" at the meeting. No one talked about the Republican Party platform's support of "right-to-work" laws, which prohibit making union membership a condition of employment. No one spoke about often-voiced fears in other organized-labor quarters that a Republican administration would dismantle, or greatly reduce the power of, the Occupational Safety and Health Administration, which is responsible for protecting workers' health.

Instead, Zeller said, Reagan recalled his days as president of the Screen Actors Guild, "when he was fighting the communist attempts to take over his union" and when "some Teamsters members protected him" against threats of bodily harm. The president-elect also thanked the Teamsters for backing him this year and renewed his promise "to make jobs a priority in his administration," Zeller said.

There has been speculation that the Teamsters hope a Reagan administration would do more than that for their union, which is the target of several federal probes into alleged misuse by union officials of millions of dollars in pension funds. Such speculation is largely the legacy of the 1972 Nixon endorsement, which came after the president commuted a 13-year federal prison term for Jimmy Hoffa -- the former Teamsters head who has been missing since 1975.

"We're up against those kinds of rumors all the time," Zeller said in an interview the day before the Reagan visit. "I don't really know how you answer something like that."

About 500,000 Teamsters members in jobs ranging from law enforcement to trucking were out of work when the 20-member union executive board unanimously endorsed Reagan last month, Zeller said. He cited double-digit inflation, and said the executive board was also upset by the Carter administration's successful drive last summer to deregulate the trucking industry, which the union claims cost its members additional jobs.

Reagan, who campaigned against big government and its myriad regulations, told an Ohio Teamsters meeting in August that he thought the Carter administration's deregulation of trucking "is ill-conceived and not in the best interest of transportation requirements of the country." That pleased Teamsters leaders.

But, as Fitzsimmons explained in a recent message to union members, the endorsement came not because of "what Gov. Reagan can do for our union, but rather what he can do for the good of the entire country."