WASHINGTON (AP) _ Quentin Burdick, after 26 years as a ''who's he?'' of the U.S. Senate, is capitalizing on his newly acquired visibility and power as a ''Mr. Chairman.''

''There are 100 senators ... but only a select few can be called 'Mr. Chairman,''' Burdick, one of 20 Senate committee chairmen, says in the opening lines of a fund-raising letter sent last month to lobbyists, individuals and political action committees.

In the letter, the 78-year-old North Dakota Democrat is selling charter memberships in ''my Chairman's Club'' to raise money ''to help put me in the driver's seat'' for the 1988 reelection campaign.

Burdick writes that he finds it ''both humbling and exhilarating'' to occupy his first major leadership post: the chairmanship of the Environment and Public Works Committee, which became his because of seniority and the recapturing of the Senate by Democrats in the 1986 elections.

For $5,000, charter members receive a gold pin. A $1,000 contribution rates a silver pin. Neither pin is precious metal, but clubbers will get a chance to show them off March 12 with what Burdick is billing as a ''high-spirited reception'' at a private Capitol Hill hideaway club frequented by lobbyists.

Burdick said contributors are getting only a pin and a party. ''Look, nobody buys access to me,'' he said. ''I see every North Dakotan who comes to my office. ... Contributors get no special privilege. ... They're buying nothing. ...

''This is not really a club as such,'' he said. ''That's just a name, a handle for my fund-raising efforts.''

Burdick said he thinks it's proper to use his position to raise campaign money. ''This fund-raiser is no different from fund-raisers held every working night in this town. ... I can't do any good for North Dakota and the nation unless I get reelected. ... Look, I think my contributors think they're getting just one thing - my reelection, and I can tell you that's a worthy goal.''

David Strauss, Burdick's administrative assistant, said that between 800 and 900 letters were sent to labor unions, liberal and pro-Israel groups, North Dakota interests and the deepest pockets of Washington - corporate and trade association PACs.

''The response is wonderful,'' he said. ''The chairmanship has been enormously helpful. ... They understand that he can be influential in moving major legislation. ... All indications are we will well exceed our goal of $100,000.''

Burdick has said he intends to run for re-election in 1988, when he is expected to face opposition from fellow Democrat Rep. Byron Dorgan, North Dakota's lone member of the House.

Under campaign finance laws, congressional candidates cannot keep any of their campaign money for personal use, but Burdick was in the Senate prior to passage of the law and is considered exempt from its provisions. Senate rules forbid such diversion but carry no penalty outside the Senate.

One of the hottest issues facing Burdick's committee in the 100th Congress is acid-rain control, which finds environmental groups pushing legislation that would cost billions to electric utilities with coal-fired boilers.

The Edison Electric Institute, the utilities' trade association, was invited to join the ''Chairman's Club.'' But the four biggest environmental PACs - run by the Sierra Club, Friends of the Earth, League of Conservation Voters and Environmental Action - say they were not invited.

''That's OK,'' said Dan Becker of Environmental Action. ''I don't have any loose change right now.'' He said, however, that Burdick's ''record on the environment is one of the best.''

Strauss said that ''we're not trying to court one side of the issue or another. We're not trying to be exclusive. ... If these groups want to contribute, we would be more than happy to take their money.

''We're not shy,'' he said. ''We try to look under every rock to find these people.''

''I guess we weren't invited because we don't live under a rock,'' said Dave Baker of Friends of the Earth.

Burdick is not the only Democrat trying to use the party's Senate majority status to raise money.

Majority Leader Robert Byrd, D-W.Va., meets occasionally with people contributing $10,000 to his campaign. Sen. Lloyd Bentsen, D-Texas, formed a $10,000 breakfast club when he became chairman of the tax-writing Finance Committee, but he quickly disbanded it following a stream of news stories.

Burdick, like Byrd, supported unsuccessful legislation last year to limit the amount of money Senate candidates can accept from political action committees.

Strauss said that until the campaign finance game is changed, Burdick will play under the current rules.

''We may not like the system, but a wise senator learns to work within it,'' he said.