John W. Hinckley, who shot and wounded President Reagan in 1981, asked a U.S. District judge yesterday to allow him to leave the grounds of St. Elizabeths Hospital once a week and to move him to a "less restrictive ward."

Hinckley, who acted as his own attorney in the motion filed with Judge Barrington D. Parker, revealed that in the last two months he had been accompanied "out on the hospital grounds 20 times" and said he had "acted appropriately and without incident."

Saying he believes he has "already proven himself with grounds privileges and is now ready for limited city privileges," Hinckley said the new freedoms would be an "appropriate" extension of the "therapeutic regimes" in which he is involved.

Hinckley asked Parker to hold a hearing on his request and to allow him "approximately 10 minutes at the end of the hearing so that he may argue his case directly before the judge."

Confined to St. Elizabeths' John Howard Pavilion since June 1982 after he was found not guilty by reason of insanity of trying to assassinate Reagan, Hinckley last appeared in court in October 1984, when he asked to be allowed access to reporters and to walk the grounds for one hour each day, accompanied by hospital personnel.