Carson didn't meet the NCAA's initial academic eligibility standards and retook the ACT test, but the school recently learned he had come up just short and appealed to the NCAA.
Carson, who played at Mesa (Ariz.) High, was an ESPNU top-50 recruit and the eighth-ranked point guard in the class of 2011. He was named to the USA Basketball Under-19 world championship team this summer.
The 5-foot-10 Carson will be able to practice with the Sun Devils this season, according to the school. The team is off to a 3-5 start after a last-place finish in the Pac-10 last season.
Diamond Leung covers college basketball for ESPN.com and can be reached at email@example.com. Information from The Associated Press was used in this report.