As a junior, he was used as a backup blocking tight end behind Henry, increasing his receiving production to 10 receptions for 105 yards and 2 touchdowns.
As a senior in 1987, he shared the starting position with Henry, making 13 receptions for 137 yards and one touchdown, as part of a 12-0 undefeated team, that won the National Championship under head coach Jimmy Johnson.
Roberts was selected by the Kansas City Chiefs in the eighth-round (197th overall) of the 1988 NFL Draft. As a rookie, he started the first 7 games, before being limited with a shoulder injury that required arthroscopic surgery in the offseason. He was replaced in the starting lineupe with Jonathan Hayes.
In 1989, he was a backup behind Hayes, making 8 receptions for 55 yards and one touchdown. In 1990, he started 13 games, posting 11 receptions for 119 yards
In 1992, he contributed to Smith leading the league with 1,713 rushing yards and 18 rushing touchdowns. He missed the playoffs because of a right knee injury he suffered in the season finale against the Chicago Bears and was not a part of Super Bowl XXVII. He was replaced with Derek Tennell.