Elliott Abrams, the assistant secretary of state for international organizations, has been chosen to become the chief U.S. spokesman for human rights, it was reported yesterday.

Abrams, who joined the State Department in May, is expected to be nominated to head the human rights bureau, a post that was given assistant secretary status in the Carter administration.

The position has been vacant since President Reagan took office. He had nominated Ernest W. Lefever, an outspoken critic of the Carter administration's emphasis on human rights, but the nomination kicked up a storm in the Senate. Lefever withdrew his name from consideration in June.

The State Department had no comment on Abrams' reported selection, but it sought to throw cold water on accompanying reports that the human rights job was being downgraded at the same time. According to an initial report by United Press International, Abrams was expected to wear two hats and add the human rights bureau to his current responsibilities.

In a statement last night, the department said the human rights function would be "strengthened and reinvigorated."

"Individual rights and political liberty are at the core of our foreign policy and the Bureau of Human Rights and Humanitarian Affairs will take on new responsibilities for interagency coordination in this area," said bureau press officer Judith Jamison. "It will remain a separate bureau and not be 'folded into' any other organization."

Abrams, 33, is a former aide to Sens. Henry M. Jackson (D-Wash.) and Daniel Patrick Moynihan (D-N.Y.) and was a member of a Washington law firm immediately before joining the department. He is a graduate of Harvard College and Harvard Law School.

The status of the human rights job has been in limbo since Lefever's withdrawal. Congress elevated it to assistant secretary status in 1977 but the only one to hold that post was Patricia Derian, a Carter appointee. The State Department has been studying possible reorganization of the human rights bureau since early summer.

The Reorganization Act, however, has expired and is awaiting renewal by Congress. Until then, any genuine reorganization apparently would require separate legislation and approval by both houses of Congress. Under the act, the president could institute such changes subject to a one-house veto.

David Carliner, chairman of the International Human Rights Group, said his organization "would certainly oppose" any effort to let Abrams hold both assistant secretaryships. If that happened, he said, "a fair question would be raised by Congress as to whether giving one person two jobs isn't, in effect, eliminating one of the jobs."