Thornton has not been charged and details have not been made public.
The warrant states two detectives went to Thornton's apartment on Western Blvd. Wednesday to follow up on the case and found a marijuana cigarette, a bag with .3 grams of pot, and the strong odor of marijuana smoke. The bag was allegedly found in Thornton's bedroom.
Police said Thornton and roommate Jamor "J.J." Jones were issued misdemeanor citations for drug possession.
Thornton was arrested on an unrelated misdemeanor assault charge this summer. Police accused him in June of grabbing his girlfriend by the arm and pushing her at the school library.
He received a plea deal in the case and prosecution was deferred as long as he kept out of trouble and participated in counseling.
In a statement, NC State said Thornton has been suspended indefinitely.
"The NC State Athletics Department takes any allegation of illegal activity very seriously. We have university and athletic policies and procedures in place regarding our expectations of conduct for our
students," is said.
NC State said J.J. Jones - a reserve freshman safety - earlier had informed the coaching staff that he plans to transfer from NC State.