UNC football spokesman Kevin Best says Davis gave the order on Thursday at practice that players are forbidden from using the popular microblogging service.
The decision follows at least two instances where players were told to take down Twitter posts. Best says defensive tackle Quinton Coples and fullback Devon Ramsey both made inappropriate posts recently. Ramsey's post involved a photograph.
Best says players who currently have Twitter accounts have been told to deactivate them, and players without accounts are barred from joining the service.