The 25-year-old Scotland international was stopped by police after an incident in Gartferry Court in the town on Sunday.
He will appear at Ayr Sheriff Court later this month.
A Strathclyde Police spokesman said: "A 25-year-old is the subject of a report to the procurator fiscal in connection with an alleged assault and breach of the peace following an incident at Gartferry Court in Ayr on Sunday."
Rangers have refused to comment on the arrest.