Robertson attended Detroit's Southwestern High School where he lettered for three years and led the team to the state championship his senior year. He co-captained Southwestern his senior year and averaged 20 points and nine rebounds a game. He was also selected a high school All-American at the end of this schoolboy years.

Robertson came to WVU after spending two seasons at Eastern Arizona Junior College where he was a standout performer. At Eastern Arizona, Tony scored 21 points per game as a freshman and added eight rebounds and five assists a game. His sophomore year was equally fruitful as he averaged 23 points a game and upped his rebounds average to 10 a game while still managing to hand out six assists a contest. In his second year participating in the Dodge City Tournament, Eastern placed second and Tony set records on the way. His 93 points and 42 field goals were the most ever scored in the Western Classic and placed him on the all-tournament team. He also made the honorable mention list for All-America that year.

Going into his junior year, Robertson was going to be used at both the guard and forward positions. Furthermore, because of his 6-5 height and leaping ability, it would have been possible to insert him into the offense at either position and him be effective at both. That year he went on to average 17.9 points, 4.4 rebounds and totaled 100 assists. Returning for his senior year it was believed that his manner, style and shooting ability and his passing was going to add up to one thing- a class basketball player. It was believed that he was going to become one of the finest players in the country his senior year.