President-elect Jimmy Carter yesterday announced the appointments of three top officials in the Pentagon, while informed sources predicted a fourth Pentagon appointment which is likely to prove controversial.

The three announced by Carter:

Clifford L. Alexander Jr., 43, former candidate for mayor of Washington and an attorney in private practice here, to be Secretary of the Army. If confirmed by the Senate, Alexander will be the country's first black service secretary.

W. Graham Claytor Jr., 64, chairman of the board of the Southern Railway Co., to be Secretary of the Navy.

Thomas B. Ross, 47, former Washington bureau chief of The Chicago Sun-Times, to be assistant secretary of defense for public affairs.

The leading candidate to become assistance secretary of defense for international security affairs, sources said, is Samuel P. Huntington, a controversial professor of government at Harvard.

Huntington infuriated student activists in the 1960s because of this advocacy of the Vietnam war, and his classroom was often the scene of protests. Sources at Harvard and former students there said the protests of those years left Huntington embittered toward students.

He once threatened to sue The Harvard Crimson for publishing an advertisement paid for by the Students for a Democratic Society which called him a war criminal.

Huntington and Zbigniew Brzezinski, Carter's choice as national security adviser, once co-authored a book, "Political Power: USA/USSR."

Another apppointment announced yesterday was that of Ernest L. Boyer, chancellor of the huge New York State University system, to be commissioner of education in the Department of Health, Education and Welfare.

During the campaign Carter came out in favor of a separate department of education, but there has been no indication as to whether or when this idea will be implemented.

Boyer is now head of the largest network of colleges and universities in the country. It includes 64 campuses and 343,000 students.

Boyer's appointment was announced by a spokesman for Joseph A. Califano Jr., Secretary-designate of Health, Education and Welfare.