President Reagan formally nominated Maj. Gen. William F. Burns, a senior State Department official, yesterday to become director of the Arms Control and Disarmament Agency.

If confirmed by the Senate, Burns, 55, would replace Kenneth L. Adelman, who resigned last month to pursue private interests.

Burns, a principal deputy assistant secretary for political and military affairs, served 1981-84 and 1985-86 as the representative of the Joint Chiefs of Staff to negotiations on the Intermediate-Range Nuclear Forces (INF) Treaty signed by Reagan and Soviet leader Mikhail Gorbachev Dec. 8. He is considered by administration officials to have relatively moderate views on arms control matters.

Aides to Sen. Claiborne Pell (D-R.I.), chairman of the Senate Foreign Relations Committee, said Pell "expected to be able to support" Burns' nomination, despite a longstanding preference for appointing a civilian to such a senior arms control post.

Burns has agreed to retire from active duty in the Army once he is confirmed.

An aide to Sen. Jesse Helms, (N.C.), the committee's ranking Republican, said Helms told White House officials Wednesday he was "reserving judgment" on the nomination but was "not opposed at this time." Helms, a critic of the INF Treaty, had favored a more conservative nominee.