On June 29, when representatives of Toyota Motor Manufacturing, USA, met at the Commerce Department to lobby senior officials for a favorable trade ruling, lawyers for the Japanese auto maker included the chairman of the Republican National Committee, Frank Fahrenkopf.

Fahrenkopf, in fact, arranged the meeting attended by the late Secretary Malcolm Baldrige and Undersecretary S. Bruce Smart. He was acting as a six-figure partner in the Washington law firm of Hogan and Hartson, registered lobbyist for Toyota.

How does this square with the 11-year old RNC rule requiring the party's national chairman to be ''full-time"? It squares ''because I do not practice law,'' Fahrenkopf told us. Hogan and Hartson pays him, he explained, because ''they're betting on the future.''

But when Fahrenkopf arranged the Commerce-Toyota meeting, he was practicing law, Washington-style. His role unsettled Commerce officials and fueled Republican dismay about leadership at an RNC that is laying off employees and is unable to raise money.

Ironically, Fahrenkopf became chairman because of the 1976 ''full-time'' rule, intended to bar members of Congress from doubling as party leader. In 1983, seeking to circumvent the rule, Paul Laxalt, then a senator, became ''general chairman'' with Fahrenkopf, his political lieutenant from Nevada, named ''nominal'' RNC chairman. In fact, Laxalt turned out ''nominal'' with Fahrenkopf running the show.

Fahrenkopf as chairman has remained a board member of First Republic Bank Corp. of California. He has become ''of counsel'' to a Reno law firm. In January 1985 he joined Hogan and Hartson.

How much all this returns is something Fahrenkopf will not reveal. The RNC won't even say what it pays him. But Federal Election Commission records show he received at least $75,480.06 as chairman during the last 12-month reporting period.

''Absolutely false,'' says Fahrenkopf to word passed in Republican circles that he also gets $350,000 to $450,000 from Hogan and Hartson. According to an acquaintance, Fahrenkopf had mentioned he was seeking that figure, which seems excessive for a retainer. The Legal Times reported he is paid ''at least $100,000 a year by the firm,'' and a source close to Fahrenkopf confirms that inexact figure.

Whatever he receives, the real question is what he does for it. ''I do nothing,'' he told us, before we mentioned the Toyota meeting. ''Go down and ask them {Hogan and Hartson} when was the last time they saw me. . . . I go down there for a meeting once in a while.''

That disturbs some Republicans. ''It's hard to understand why somebody would pay a six-figure salary for somebody doing nothing,'' said Richard Richards, who told us he turned down two law-firm offers while serving as national chairman immediately preceding Fahrenkopf. According to the Legal Times, Hogan and Hartson ''has paraded Fahrenkopf before potential clients, some of whom have retained the firm. . . .''

While the firm considers its relationship with Fahrenkopf an investment in the future, part of that future is now. The June 29 meeting was arranged for Toyota lobbyists to press on Commerce officials a ''free trade zone'' in connection with the company's new auto plant near Lexington, Ky.

When we raised this with Fahrenkopf, he replied: ''I talked to Mac {Baldrige} and to Bruce Smart and said, 'Arrange a meeting.' Would they sit down with a representative of Hogan and Hartson to discuss the foreign trade zone issue? I said I was not going to be there as an advocate. I did not argue. . . . All I did was arrange it.''

Fahrenkopf called this ''very unusual,'' saying, ''I can't think of another time {he had so acted}. I try to be very, very careful.'' Why this time? It was of ''some urgency'' to get the trade zone application ''moved along.''

Move it he did. On July 13, the Commerce Department set an Aug. 12 hearing on Toyota's application. A senior official present June 29 recalled Fahrenkopf saying little. But at the Commerce Department, there was unease on two scores: that the Republican national chairman arranged the meeting and that he attended it.

''If someone's telling you I'm practicing law at the same time I'm doing this {the chairmanship} and therefore violating the rules,'' Fahrenkopf told us, ''that's bull . . .'' But his helping to lobby the Commerce Department provides ammunition for his critics.