City police spokesman Jody Donaldson said Crapo, 61, posted a $1,000 unsecured bond and faces a Jan. 4 court date, the Washington publication Roll Call reported.
Police said an officer witnessed Crapo run a red light and pulled him over at 12:45 a.m. Crapo allegedly failed several field sobriety tests and was arrested.
The three-term senator, who previously served three terms in the U.S. House, issued an apology Sunday evening.
"I am deeply sorry for the actions that resulted in this circumstance," he said. "I made a mistake for which I apologize to my family, my Idaho constituents and any others who have put their trust in me. I accept total responsibility and will deal with whatever penalty comes my way in this matter. I will also undertake measures to ensure that this circumstance is never repeated."