The Rev. Gerry Nugent, 63, made the admission while testifying Tuesday at the rape and murder trial of church handyman Peter Tobin, 60.
Tobin is accused in the death of 23-year-old Polish student Angelika Kluk, whose body was found under the floor of St. Patrick's Church in Glasgow last September.
Nugent testified that Kluk was staying at his chapel house when he began an affair with her, The Times of London reported.
"The sexual intimacy happened about three or four times. I felt guilty and I felt ashamed and disgusted with myself," he said.
The priest said, at the request of the archbishop, he resigned his position at St. Patrick's two weeks ago and is undergoing therapy for alcoholism.
Tobin has entered a plea of innocent in the trial, which continued Wednesday.
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'