President Reagan yesterday nominated Robert H. Bork -- the solicitor general who carried out President Nixon's order to fire the Watergate special prosecutor in the 1973 "Saturday Night Massacre" -- to the U.S. Court of Appeals for the District of Columbia.

If he is confirmed by the Senate, Bork would succeed U.S. Circuit Judge Carl E. McGowan on the 11-member court.

Bork, a long-time constitutional law professor at Yale University, recently joined the Washington law firm of Kirkland & Ellis.

His appointment would add a conservative voice on the influential appellate court here, which has long had a reputation for liberalism. Four of the most recent appointees were namedby former president Carter, and all are regarded as liberal.

Widely respected in academic circles, Bork received the highest possible ranking for the job by the American Bar Association review committee, White House counsel Fred Fielding said yesterday.

On Oct. 20, 1973, in one of the most dramatic incidents of the Watergate era, Attorney General Elliot Richardson resigned and his deputy, Donald Rumsfeld, was fired for refusing to carry out Nixon's order to fire Watergate prosecutor Archibald Cox. Bork became acting attorney general and fired the prosecutor, who had refused to give up efforts to obtain tapes relating to the case.