Yale law professor Eugene V. Rostow has accepted a White House offer to head the U.S. Arms Control and Disarmament Agency (ACDA). informed sources said yesterday.

Rostow is a longtime Democrat who served in the Johnson administration as undersecretary of state from 1966 to '69 but supported the Republican ticket during the 1980 election campaign.

The Reagan administration has not completed internal deliberations on arms control policy toward the Soviet Union, and some officials say one reason those discussions have lagged is that no ACDA head has been named.

rostow's name emerged only recently as a candidate for the post after enthusiasm within the administration began to wane for retired Army Lt. Gen. Edward Rowny.

Rostow, 67, has held hawkish views on defense and foreign policy for many years and served as chairman of the Committee on the Present Danger, a bipartisan group of current and former officials who felt that the United States had let its defenses slip dangerously and was pursuing questionable foreign policies.

At a committee press conference last October, Rostow told reporters he wanted to explain "why a devout Democrat like me is speaking for Gov. Reagan." He went on:

"I am immensely concerned about the risks of war. I don't agree with Gov. Reagan on a number of domestic issues, but the problems of preserving the peace . . . are infinitely more important than all our other problems put together."

Rostow would face Senate confirmation hearings. Some conservative lawmakers, who favor Rowny, have threatened to hold up on Rostow's confirmation.