Roberts attended Lower Richland High School in Hopkins, South Carolina, where he led his team to two straight state championships, was a Parade first-team All-American his senior year, and considered a top five player nationally, holding his own against Alonzo Mourning in the Dapper Dan and McDonald's All-Star Games. Subsequently he played collegiately at Louisiana State University, teaming up in his second (and last) season with Shaquille O'Neal. He spent 1990-91 with Real Madrid, alongside Carl Herrera.
Roberts was selected by the Orlando Magic in the 1st round (23rd overall) of the 1991 NBA Draft, and went on to appear, in a career marred by injuries and other drawbacks, for the Magic, Los Angeles Clippers, Minnesota Timberwolves, Houston Rockets and Philadelphia 76ers in eight NBA seasons from 1991-1999. His best year as a pro came during his first year with the Clippers, when he appeared in 77 games and averaged 11.3 ppg and 62 rpg, with 141 blocked shots.
Roberts missed all but 14 games in the 1993-94 season, then all of the next season, due to an Achilles tendon injury, first in one leg, then the other. Amazingly, he still bounced back for three more respectable seasons.
After an unassuming 6-game spell with the Rockets, as a member of the 76ers in late 1999, Roberts was banned by the NBA for drug violations.