Parrish attended the University of Washington, where he played for the Washington Huskies football team from 1993 to 1997 in the Pacific-10 Conference and majored in psychology. He redshirted as a true freshman, and then went on to record 21 tackles and two interceptions during his first year of playing. As a sophomore and freshman, Parrish started a combined eight games at strong safety. He then went on to start every game as a junior at free safety. Parrish was named first-team All-PAC-10, recording 71 tackles, along with two forced fumbles, four fumble recoveries, eight passes defended, and two interceptions.