George Archer, playing his best golf since a back operation in 1978, shot a course-record 66 to win the third annual Fellowship of Christian Athletes Golf Pro-Am yesterday at Country Club of Fairfax before a crowd of about 3,000.

Archer edged Washington pro Lee Elder, Greg Powers, and Mike Sullivan, who all shot 67. J. C. Snead, last year's champion, shot 68.

Archer, a tour veteran from Gilroy, Calif., said, "I think I am swinging better than I ever have." He finished third in the Memorial Tournament in Dublin, Ohio, over the weekend and will play in the Kemper Open, beginning Thursday at Congressional.

After his operation, Archer missed virtually all of the 1979 season. He said he has worked hard to get his game back into shape and has had good showings this spring, including an 11th-place finish in the Masters.

Archer started at the second hole in the shotgun start event. He holed out a shot from a greenside sand trap for a birdie at the eighth hole. On the par-5 ninth hole, he made eagle 3 by sinking a 35-foot putt. Archer bogeyed the 10th hole but made two more birdies and parred the rest.

Elder was four under par for 14 holes, but drove behind trees and took his only bogey on the 15th hole to fall two shots behind Archer. Elder birdied the ninth hole to pull within one but parred the 10th hole, his finishing hole.

Amateurs paid $500 apiece to participate and mix with golf's best, including Gary Player, Gene Littler and Larry Nelson, who were warming up for the Kemper. Coach Tom Landry of the Dallas Cowboys also played.

Nelson and Player conducted a clinic before the tournament and Player, one of the world's best sand players, gave a less to Redskin quarterback Joe Theismann, who shot 87. Nelson gave putting tips to Redskin Coach Joe Gibbs.

The purse was changed this year for the field of 108 amateurs and 27 PGA pros. The total purse was reduced from $10,000 to $3,000, with Archer receiving $600.