For the first time in 10 years, the Corcoran Gallery of Art has named a new director who is an experienced museum executive, not a relative beginner.

He is Michael Botwinick, 38, who has been director of the Brooklyn Museum since 1974. He says he joined the Corcoran because he is "convinced that it is an institution on the verge of taking off."

His appointment, approved yesterday by the Corcoran's trustees, is effective Jan. 1. He succeeds Peter Marzio, who will leave Oct. 1 to assume the directorship of the Houston Museum of Fine Arts. Edward J. Nygren, the Corcoran's curator of collections, will serve as acting director until Botwinick arrives.

That Botwinick agreed to leave an art museum almost twice as large says something about the Corcoran's steadily increasing stability, financial health and national prestige. "People in Washington," he said, "do not yet see how far the Corcoran has come -- and that it is on the brink of asserting itself."

This city lured him, too. "Washington," he said, "may be the most exciting museum town in the world -- not the country, but the world.

"I come with no program," Botwinick said. "I have no exhibits in my pocket, no curators to hire, no pictures to acquire. Having said that, let me say I do have goals: The first is to see the Corcoran assert itself as a national museum. The second is financial. When the museum-support community begins to realize what a gem this institution is, as I have, there will be a quantum leap in gifts, in the number of checks and the amount of those checks. The third is to solve the space problem. We can't take the Renwick back. The Executive Office Building is not available. But the Corcoran has to grow. It's too big for its envelope. The fourth is to serve this city and its artists. The Corcoran is the only place in town that has a fair claim to being the city's own museum."

The Corcoran, once plagued by budget deficits, was able to avoid them during Marzio's regime. Attendance rose from 85,000 during 1977, the year before he came, to about 500,000 in 1981. The Corcoran, which raised $920,000 the year before he came, raised $2.7 million in 1981-82, though much of that amount was spent on a new air-conditioning system, now being installed.

Botwinick said, "Peter Marzio has left the Corcoran in super shape." Marzio, however, had never run an art museum before he took the job. He was a curator of prints and drawings at the Smithsonian Institution's Museum of History and Technology when hired by the Corcoran. His immediate predecessors, trustee Gilbert Kinney, who served as acting director in 1977, and Roy Slade, who ran the Corcoran from 1972 to 1977, had even less experience. Slade was an artist and art teacher employed as dean of the Corcoran School of Art when named to the directorship.

Botwinick, in contrast, has strong museum credentials. He was assistant director for art at the Philadelphia Museum of Art from 1971 to 1974, and assistant curator in chief at the Metropolitan Museum of Art in 1971. Before that he was assistant curator and associate curator for Medieval Art and the Cloisters at the Met.

The Brooklyn Museum, housed in a six-story neoclassical building designed by McKim Mead and White, has an annual operating budget of $7.5 million. The Corcoran's budget, for both its gallery and school, is now about $4 million.

"I could have stayed there for a good long time, but not forever," Botwinick said. "I was not on the verge of being shown the door. Leaving Brooklyn was the only way to get here.

"If there is something that I am proud of in Brooklyn--and hope to transfer to the Corcoran--it was that I was viewed by my curators and staff as the person who makes things happen. The director has to orchestrate. My time in Brooklyn was divided in three halves: I spent half of it on fund-raising, half on administration and half on artistic matters."

Botwinick says that in 1974, the year he went to Brooklyn, the museum raised "$30,000 for general operations, toilet paper and soap. Last year the comparable figure was $860,000."

He is highly regarded by many of his peers. Washington museum directors Marzio, Abram Lerner of the Hirshhorn and J. Carter Brown of the National Gallery recommended his appointment, said David Lloyd Kreeger, president of the Corcoran's trustees.

Evan Turner, who will succeed Sherman Lee as director at Cleveland, and who was director of the Philadelphia Museum while Botwinick was there, calls him "absolutely top-notch. He has brilliant acumen in overall administration. When he came to Philadelphia we were planning to air-condition the building, and he emceed the whole thing. He charted a route for us through complicated financial waters. He's a master at honing a budget."

"I think he's marvelous," said Anne d'Harnoncourt, now the Philadelphia's director. "Michael is a pro," said Henry Geldzahler, who knew him at the Met and is now commissioner of cultural affairs for the city of New York. "The Corcoran was lucky to get someone of his experience and imagination."

In the last years of the '60s, and in the early '70s, such Corcoran directors as James Harithas and Walter Hopps stamped their own esthetics on most Gallery exhibits. But Botwinick, like Marzio, will not do shows himself.

"Northern Light," the Corcoran's current exhibit of Scandinavian painting, was organized by the Brooklyn Museum. While Botwinick was there, Brooklyn showed "The Dinner Party" by Judy Chicago, "Woman Artists 1650-1950," David Driscoll's "Two Centuries of Black American Art," the Corcoran's own Black Folk Art exhibition, "Belgian Art 1870-1900," "Africa in Antiquity: The Arts of Ancient Nubia and the Sudan," and work by such contemporaries as Gene Davis, Romare Bearden and Sol LeWitt.

The Corcoran's search committee was headed by trustee Freeborn G. Jewett Jr., who said Botwinick's "record is solid" and his "personality is delightful." The committee, said Botwinick, "made me an extremely serious offer." His Corcoran salary was not disclosed, but he said it will be 5 percent higher than it was in Brooklyn. "We went for the best man available and paid what it took to get him," Kreeger said.