Taxpayers this year will be cleaning up at the Corcoran Gallery of Art President Carter yesterday signed into law a bill giving $200,000 or more -- for janitorial services and similar expenses -- to the private museum, which never has received such support before.

The one-year grant, to be disbursed by the National Park Service, was hailed as "a vote of confidence in our museum" by Corcoran President David Lloyd Kreeger. "I think we've turned the corner," Kreeger said. "It is easier to raise money for a healthy institution than it is for one that's sick."

The Corcoran will get at least $200,000 from the Park Service -- and it may receive $100,000 more. The Corcoran, the Folger Shakespeare Library and Arena Stage, all private institutions, together lobbied for the bill the president signed yesterday. The total of $600,000 which it appropriates only can be given to institutions that qualify as "historic sites."

Arena does not yet have such a designation, and because it is so young is unlikely to receive one. If it doesn't, the Corcoran and the Folger will get $300,000 each. Should the secretary of the Interior grant Arena a "historic site" designation, the $600,000 will be split into thirds.

In terms of gifts (which have grown greatly), attendance (which has tripled) and deficits (which have vanished), the Corcoran is stronger now than it has been in years:

More than $1 million was raised by the museum in the fiscal year that ended last Sept. 1. That is more than four times as much as the Corcoran received in 1974 -- the year Kreeger became president -- and an increase of more than $450,000 over fiscal 1978.

Only a few years ago the museum had so little cash that it stopped buying costly works of art. But that is true no loner. Last May the museum auctioned off some rarely shown European pictures for $671,000. That money will be spent on American works of art. Two impressive paintings -- a rare 1917 cubist painting by Max Weber ($65,000) and an 1876 painting of a waterfall by DeWitt Clinton Boutelle, "Trenton Falls" -- have been bought this year.

Last year, for the first time in recent memory, the Corcoran showed an operating surplus of $39,000. It also added $60,000 to its small endowment. In 1973, the museum's deficit was a staggering $385,867, but since 1976 the Corcoran's books generally have been in the black.

Last year's attendance was about 150,000. Since May, when the museum -- aided by a 10-year, $1,150,000 pledge from Dr. Armand Hammer -- instituted a free admissions policy, attendance has been running three times the previous rate.

Other benefactors, both private and governmental, have been giving to the Corcoran. Three $100,000 grants (which must be matched on a two-to-one basis) have come from the Cafritz Foundation since 1977. The federal Institute of Museum Services has given $50,000. $350,000 (which must be matched on a three-to-one basis) has come from the National Endowment for the Arts. And an anonymous "unitrust gift" of $500,000 was received last year.

"There is a lot of good news, true, but 'iM still worried," said Peter Marzio, the Corcoran's director. "To keep up the good work, we're going to have to raise $1.4 million this year. Our endowment is still small -- it was up to $5 million before it was eroded by all those years of deficits, but it is only $3.5 million now.

"Our costs are now so high, and our institution is so fragile, that with one bad year we'd be licking our wounds for the next decade."