Eight persons were arrested yesterday after demonstrators demanding changes in President Reagan's policies concerning servicemen missing in action in the Vietnam War handcuffed themselves to a White House gate until U.S. Park Police officers ended the protest.

The demonstration at 10:50 a.m. was sponsored by the National Vietnam Veterans Coalition of the Sons and Daughters of MIAs, said Tom Burch, head of the coalition.

The five women and three men were charged with disorderly conduct after what police spokesmen said was a brief, nonviolent demonstration. They were released after each paid a $10 fine.

Observers said the demonstration was subdued and that those involved offered no resistance to police at the time of their arrest.

Almost 2,500 persons are still listed as missing after the Vietnam War. Although most have been declared dead, there are still recurring reports that some prisoners of war are being held in Southeast Asia.

Officially, the United States investigates each report, and the government's position is that it cannot rule out the possibility that some POWs remain. President Reagan has said a full accounting of the MIAs is one of his highest priorities.

Burch said protesters want an independent congressional commisison created to review the evidence regarding POW reports.