Morris' first acting role was as a child when he appeared in the 1966 Star Trek episode "Miri". Star Trek was, at the time, shot at the same studio that produced Mission: Impossible, where his father was working. He made his feature film debut in Star Trek III: The Search for Spock in a small role and later guest-starred on Star Trek: Deep Space Nine and Star Trek: Voyager.
In the mid-1980s, he portrayed law student (later attorney) Tyrone Jackson on the CBS daytime drama The Young and the Restless. During a major storyline, his character used heavy theatrical make-up to appear Caucasian, in order to go undercover to expose an organized crime organization.
Morris played one of Will Smith's college professors on the NBC show The Fresh Prince of Bel-Air and played Dr. Clay Spencer on the then-UPN television show Girlfriends. In the January 25, 2007, episode of the The CW television series Smallville, Morris also portrayed the DC Comics superhero The Martian Manhunter/John Jones, which is a recurring but small character in the series so far. He reprised that role on the show's sixth season finale on May 17, 2007, as well as the episodes "Bizarro" and "Cure" in the seventh season and the episodes "Odyssey", "Prey" and "Bulletproof" in the eighth season. He reprises this role in the ninth season episodes "Absolute Justice", "Checkmate" and "Salvation". As a voice actor, he portrayed the villains Imperiex on Legion of Superheroes, and as the Immortal Caveman Vandal Savage on Justice League and Justice League Unlimited. He appeared on one episode each of the series CSI: Miami and Seven Days. Though largely unnoticed, Morris also was the voice of Paul the Apostle in Zondervan's The Bible Experience. Morris also made a cameo appearance as the late Miles Dyson in photographs in the television series Terminator: The Sarah Connor Chronicles. He played the voice of the character 'Doc Saturday' in the animated show The Secret Saturdays. He also played a major supporting role in the PlayStation 2 game Ratchet: Deadlocked, Merc, one of the combat bots that accompany Ratchet during his journey. He also voiced the character of "Thurgood Stubbs" on the animated show The PJs, after Eddie Murphy's departure.