Cindy Davis of Prince Georges, owner of a sweet swing and a deft putting stroke, was three under par for the necessary 15 holes as she beat Kim Williams of Bethesda, 4 and 3, yesterday to win the Women's District Golf Association championship at Woodmont Country Club's North Course.

The 21-year-old Furman all-America added the WDGA title to her Maryland Women's Amateur championship. Davis, whose family will move in two weeks from Bowie to a condominium bordering Prince Georges Country Club, also won the Middle Atlantic women's title in 1980 and 1981.

Davis also said she is planning a professional golf career in the mold of Furman greats Betsy King and Beth Daniel.

Williams birdied the first hole for a 1-up lead. Davis, who said she was tentative early and did not loosen up until the third hole, birdied the fourth to even the match. Two more birdies for a two-under-par 35 left Davis with a 1-up advantage after the front nine.

Davis took complete control after Williams three-putted the 11th hole from 30 feet to go two down. Davis sank a tricky, downhill, six-foot par putt to halve the 12th hole, and took a 3-up lead with a six-foot birdie putt at the par-3 13th hole after an outstanding tee shot.

Davis brought the match to a close by sinking a downhill, 20-foot birdie putt at the par-5 15th hole.