He began his college career playing football at the NCAA Division II level at Northwood University. He appeared in 8 games in 2010 as a freshman, making 22 tackles (one for loss) and one forced fumble. After the season, he transferred to Riverside City College in his hometown

As a sophomore he started 11 games, registering 88 tackles (second on the team), 13 tackles for loss, 1.5 sacks, 4 fumble recoveries, 3 interceptions (one returned for a 75-yard touchdown), while helping the team to a perfect 11–0 record and a number 5 national ranking. At the end of the year, he announced his intention to transfer to NCAA Division I Texas Tech University in 2012.

As a junior, he played in all 13 games (11 starts), collecting 55 tackles (1.5 for loss), 34 solo tackles and 3 quarterback hurries. His performance would earn him a third-team All-Big 12 selection by Phil Steele and an honorable-mention by the AP.[1]

Smith's senior season in 2013 earned him several accolades. He started 13 games, posting 120 tackles (third in the conference), 86 solo tackles (led the conference), 10.5 tackles for loss, 4.5 sacks, and a fumble return for a touchdown. He had 18 tackles against the University of Texas. His mark of 120 tackles was the most by a Red Raider since the NCAA record setting Lawrence Flugence's 193 in 2002.

For his performances throughout the season, Smith earned Holiday Bowl defensive MVP honors, as well as first-team All-Big 12 Conference selections by the Associated Press and the Big 12 Broadcasters.