The chief judge of U.S. District Court here yesterday approved a long-awaited agreement that orders the District government to start paying out $2.2 million in damages to more than 900 antiwar demonstrators who were arrested on the Capitol steps during a massive May Day protest 10 years ago.

The protesters, along with thousands of others, swarmed into Washington for three days in May 1971 to rally against the Vietnam War. Each of the 900 will receive $750 for violation of his right of free speech, and additional sums -- ranging from $120 to $1,800 -- for a claim of false arrest and imprisonment.

The settlement agreement, signed yesterday by Chief Judge William B. Bryant, marks the end of an extended class action lawsuit that stemmed from arrests made as Rep. Ronald V. Dellums (D-Calif.) was speaking to a crowd on the east steps of the Capitol on May 5, 1971.

In 1975, a federal jury awarded more that $12 million to the demonstrators, but two years later the federal court of appeals ordered the damage award to be reduced. In December 1979, Bryant set the lower figures that were laid out in the agreement he approved yesterday. Since then attorneys for the city government, the Justice Department and the protesters have tried to determine who should get how much money and when.

Meanwhile, in December 1980, Congress appropriated $3.15 million to the District government to cover the May 5 damage payments as well as additional damages owed to about 350 other protesters who sued for their arrests on May 3 and May 4, 1971. Those lawsuits were settled out of court.

Arthur B. Spitzer, legal director for the Washington chapter of the American Civil Liberties Union, said yesterday that checks will be sent to all of the May 5 protesters who can be located. The ACLU, which has a list of names of persons who are involved in the lawsuit, has lost track of some of the protesters, Spitzer said.

In addition to the $750 damage award for the free-speech violation, the court also set out a graduated scale of additional damages for false arrest to be paid on the number of hours each person was incarcerated. For example, person held for 12 hours or less will receive $120 each, while those held for more that 48 hours will get $1,800.

The protesters had sued the city government, the chief of the U.S. Capitol Police and the District police chief.