Mrkonic played college football at the University of Kansas from 1950 to 1952. During that period, the Jayhawks had a 21–9 record. They finished 8–2 in 1951, the year he was selected as an All-American. Mrkonic was selected on the all-conference team in 1950 and 1951. He was also the punter for the Jayhawks, and led Kansas in punting stats in 1951.