Mr. Crapo, 61, has a Jan. 4 court date.

“I am deeply sorry for the actions that resulted in this circumstance,” he said in a statement on Sunday night. “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.”

A spokesman for Mr. Crapo declined to comment on the circumstances surrounding his arrest.

Mr. Crapo has been in the Senate since 1999, and served for six years in the House of Representatives before that. He was easily re-elected in 2010, and will not have to run again until 2016.

In Congress, Mr. Crapo has built a reputation as a staunch social and fiscal conservative. It has been expected that he would take over the top Republican spot next year on the Senate Banking Committee.

Mr. Crapo also serves on the Senate’s budget and finance panels, and was one of the “Gang of Six” senators who worked in 2011 toward a deficit-reduction deal that was never adopted by Congress.