Adam, 20, the brother of Scotland international Charlie Adam, is alleged to have committed the offence outside a nightclub, in Glasgow's Merchant City area, early on Sunday.
Grant Adam has been with the Scottish champions since leaving school and is the club's third-choice keeper.
He is due to appear at Glasgow Sheriff Court on Monday morning.
A spokeswoman for Strathclyde Police said: "We can confirm a 20-year-old male has been charged in connection with an alleged sectarian breach of the peace, in relation to an incident in Ingram Street on Sunday 6 November."
A spokesman for Rangers said the club would also investigate the allegation.
He said: "We are aware that a player was arrested and we will investigate the matter fully before we make a comment".
