Perry was stopped Tuesday evening on Wade Avenue and Woodburn Road after an officer spotted him driving erratically.
Court records indicate that he registered a 0.09 on a breath alcohol test. The legal limit in North Carolina is 0.08.
Perry, a democrat, is a lawyer who represents criminal defendants.
He tells Eyewitness News he has not made a decision on whether he will continue his candidacy.
"I made a mistake for which I take full responsibility," he said. "The death of my father four weeks ago after an extended illness, impacted me in a far greater way than I ever imagined possible. I apologize to the people of Wake County and for their understanding. I still believe in the presumption of innocence, of due process, and the equal protection of law, and I always will."