The arms control and Disarmament Agency last month proposed to the White House that the Reagan administration "should begin an immediate media campaign" to deal with "the growing stridency and hysteria" of the antinuclear weapons movement.

In a memorandum from Eugene V. Rostow, director of ACDA, to William P. Clark, the national security tr oufadviser, the agency said that Ground Zero Week, a national educational campaign on the dangers of nuclear war, would produce an "eruption of the issue of nuclear war."

A copy of the memorandum was sent anonymously to The Washington Post, and its authenticity was confirmed by the agency. Portions of it appear on page C4.

"The press and electronic media will be full of demagoguery and emotion as journalists hungrily interview tearful mothers and self-righteously indignant clergymen against a mushroom cloud background," the ACDA memo predicted.

To counteract this publicity, ACDA proposed a series of op-ed articles and television appearances by friends of the administration and statements by administration officials. The memo proposed that these appear daily from April 17 to 26, starting before and ending after Ground Zero Week activities.

The White House apparently rejected the specific advice contained in the Rostow memorandum, choosing not to react extensively to Ground Zero Week. Some of the general ideas the memo contained -- for example, using Vice President Bush as an administration spokesman to respond to the antinuclear weapons movement -- were used. None of the specific events described in the proposed schedule printed on page C4 actually occurred, as far as The Washington Post could determine.

The "eruption" of the antinuclear issue the memo predicted also failed to materialize. Although Ground Zero week promoted extensive media coverage and activities attended by hundreds of thousands of Americans, it produced no great outpouring of popular feeling.

The ACDA memo warned that the nuclear war issue was infecting the public. "While this movement includes such perennial elements as the old-line pacifists, the environmentalists, the disaffected left and various communist elements," the memo said, "there is participation, on an increasing scale in the U.S., of three groups whose potential impact should be cause for concern. They are the churches, the 'loyal opposition' and, perhaps most important, the unpoliticized public."