"Back to the Future," the Steven Spielberg-produced box-office-smash movie that the Academy Awards is ignoring this year, was named the best picture of 1985 and its star, Michael J. Fox, the best actor Saturday at the Your Choice for the Film Awards. The 21st annual awards, produced by RKO television and compiled from a survey of theater owners nationwide, also named Cher as best actress for her role in "Mask."

When asked to name the best picture, the theater owners selected "Back to the Future," the comedy about a teen-age time traveler that as of Feb. 11 had grossed a staggering $199 million. The other nominees were "Cocoon," "The Color Purple," "Out of Africa" and "Witness." The 24-year-old Fox beat out Harrison Ford of "Witness," Jack Nicholson of "Prizzi's Honor," Robert Redford of "Out of Africa" and Sylvester Stallone of "Rambo" fame. Not a bad group for a newcomer to compete against. Best supporting actor went to Don Ameche, who has not worked much in recent years, for "Cocoon," with best supporting actress going to Chicago television talk show host Oprah Winfrey in her first movie, "The Color Purple."

Honors for Abigail McCarthy

Washington author Abigail McCarthy is to be in St. Paul, Minn., today to see the Abigail Quigley McCarthy Women's Center dedicated at her alma mater, the College of St. Catherine. The center, at what is described as one of the country's largest women's colleges, is a place of research and scholarship for women. Catherine Lupori, director of the center, said the ex-wife of former senator Eugene McCarthy was selected for the honor because "in both her private and professional life she has given outstanding testimony to the potential of women."

McCarthy, who has been writing a column for 15 years for Commonweal magazine, has written both fiction and nonfiction books. She has a new novel about to be published, cowritten with Jane Muskie, wife of former senator Edmund Muskie, about a political wife who is fighting against political forces who are trying to have her committed to a mental institution, an idea stimulated by an event in the life ofthe late Martha Mitchell, wife of former attorney general John Mitchell.

End Notes

Actress Elizabeth Ashley was arrested at Edmonton International Airport Friday and charged with two counts of narcotics possession. She was arrested when she arrived at the Canadian airport on a flight from Los Angeles. The reason for the arrest was not detailed. She was held for more than 12 hours and released when $7,500 bail was posted. She flew to Edmonton, Alberta, to meet with actress Sandy Dennis, who is performing in a play there. The two actresses are scheduled to fly to Baltimore on Tuesday to begin rehearsals of the comedy "A Coupla White Chicks Sitting Around Talking" at the Morris A. Mechanic Theatre . . .

When Catholic University's Father Hartke died two weeks ago, plans were under way for a Golden Jubilee to celebrate his 50 years as a Dominican priest. Hartke had wanted to use the celebration as one last fund-raising effort for his scholarship fund, and artist Betty Dunston had created a bronze bust of Hartke in a signed limited edition and a commemorative medallion. The Dominican House of Studies has decided to carry on the plans by making the bust and medallion available to those who want to contribute in memory of the priest of Washington theater . . .

Country singer Mickey Gilley celebrated his 50th birthday yesterday and the 15th anniversary of his beer joint in Pasadena, Tex., billed as the world's largest nightclub. And to the usual question of how he feels about the milestone: "I never dreamed I'd ever make it half a century, but it was through good music, good women and great booze." That'll do it every time . . .