President Carter Yesterday signed a bill making the Museum of African Art. worth an estimated $10 million, a department of the Smithsonian Institution.

The museum was founded 14 years ago by Warren Robbins, a former Foreign Service officer. Its dowry includes: a $5.5-million collection of some 7,000 African sculptures, paintings and decorative objects: and $1 million photographic archieves of famed Life photographer Eliot Elisofon: the $1-million collection of Afro-American paintings of the 19th century, including 60 works by Henry Tanner, and a $2.5-million row of nine Capitol Hill townhouses.

The figures, compiled by Robbins, are from Smithsonian appraisals, insurance evoluations and tax assessments.

The staff of about 42, headed by Robbins as director, will stay on. The bill provides for a current annual budget of about $1 million, a fourth of which will be raised by the museum from private sources.

The museum, whose initial home was the Frederick Douglass house, the home of a post Civil War black leader, is host to 1,000 to 2,000 visitors a extensive education program in the city schools.

Carter's statement on the signing said, according to the Associated Press, the museum "has amassed a remarkable collection of traditional African art objects, all of which are being donated to the people of the United States. Thanks in no small part to the effective programs of the Museum of African Art, the magnificent creations of the cultures of Africa have now been recognized as forming one of the truly major art traditions of the world."

About three years ago, Robbins, who said he was tired of the difficulties of fund raising, approached the Smithsonian with the idea of becoming a department. The Smithsonian, at that time under criticism for initiating new program without informing Congress, was interested, but only if Congressional approval was assured.

Robbins then went to work, principally with the help of the late Sen. Hubert H. Humphrey, for several years chairman of the museum's board; Sen. Wendell Anderson (D-Minn.) Sen. Claiborne Pell (D-R.I.) and Reps. Lindy Boggs (D-La.) and John Brademas (D-Ind.) and the Black Caucus.

Smithsonian Secretary S. Dillon Ripley, in welcoming the new museum said, "The Museum of African art fills a serious gap in the Institution's coverage of the world's major artistic traditions and contributions. The museum also offers great potential as a study center . . . "