Plummer accepted a football scholarship to Arizona State University in Tempe. He did not redshirt and took over as the starting quarterback (from Grady Benton) early in his freshman season in 1993. He had consistent, but not outstanding, statistical output during his career, and never led the Pac-10 in any major statistical category. He threw for an impressive 1,650 yards in his freshman season, but also had seven interceptions to just nine touchdowns. He broke 2,000 yards in 1994 as a sophomore, and upped his touchdowns to 15. As a junior in 1995, his 2,222 yards and 17 touchdowns, many coming at pivotal moments in games, earned him a strong fan-base and all-conference honors despite a lackluster 6–5 record.