Commerce Secretary Malcolm Baldrige shook hands gingerly at a congressional fund raiser here last night, protecting his right thumb broken Sunday while competing in a rodeo.

Later, while about 100 party faithful stood around a paneled room decorated with the banners of Big 10 schools, Baldrige pressed for the election to the House of Tom Ritter, a young businessman running against Democratic incumbent Bob Carr.

"Tell all your Democratic and independent friends who are going to vote for the president, and there are a lot of them, to send Republicans like Tom Ritter to Congress to get his program through," Baldrige said.

"The president needs Tom in there to back him."

Baldrige carried the message in five stops in Michigan that President Reagan had brought the country to economic prosperity and now needs the help of more Republican congressmen so he can finish the job. The Michigan trip, one of about 70 the Commerce secretary has made during the campaign, was easier than some, with only three press conferences and two speeches in an 8 1/2-hour day.

He said it was nothing compared with a recent day of campaigning that started with a 5:30 a.m. flight from Washington for a breakfast in Chicago and continued with a mid-morning rally in St. Paul, Minn., a luncheon in Des Moines and an afternoon appearance in St. Charles, Mo.

Baldrige's aides called these appearances unglamorous and said they were designed largely to get local publicity for the Reagan-Bush ticket and the congressional candidate. But they are run with all the snap of a well-organized campaign, including young advance men from the Reagan-Bush operation at every stop.

Baldrige on the campaign trail is low-key, a businessman of 30 years' experience who seems to relate well to the Republican audiences he faces, but is not one of the best recognized figures of the Reagan administration.

An airport security guard in Detroit, for instance, was wowed by his large championship rodeo belt buckle that set off the metal detector, but never realized that the man wearing it was a member of the Reagan Cabinet.

Baldrige derides his ability as a speechmaker. "I'm probably not the best public speaker in the world, so I hope I won't set Bill back," he told a press conference at the airport at Saginaw, Mich., where he stopped on behalf of Bill Schuette, the Republican candidate for the congressional seat held by Rep. Donald J. Albosta (D-Mich.).

But he holds his audience and scores points for the administration in his press conferences. He has the politician's knack of quickly learning the key issues in a congressional race and relating them to the GOP candidate. He is not afraid, moreover, to attack domestic content legislation, designed to reduce the number of foreign-made cars sold in the United States, in a state where the auto industry is number one.

Baldrige was sent out by the Reagan-Bush campaign apparatus that focuses on key congressional races. Although both Ritter and Schuette are underdogs, their campaigns were listed by The Detroit News as the Republicans' best chances in Michigan to capture congressional seats held by Democrats.

Vice President George Bush and Agriculture Secretary John Block also have appeared for Schuette, which the candidate said "is a statement, it's a signal."

Schuette arranged a Baldrige speech at Northwood Institute, a business college in Midland, Mich., that drew 1,000 students who were given time off from classes. Baldrige struck the familiar themes of the Reagan campaign, boosting the president's economic successes and attacking tax increases proposed by Walter Mondale. He also contrasted what he said was the orientation of the administration for "freer trade" with Mondale's "protectionism."