Spencer was arrested on preliminary charges of public intoxication and disorderly conduct about 3 a.m. Sunday outside the Have a Nice Day Cafe, city police Sgt. Matthew Mount said.
Spencer, 24, was later released without bond. A court appearance was scheduled for Jan. 15.
Police said Spencer and another man were thrown out of the bar when they refused to leave at closing time, then argued with officers and ignored orders to leave.
A bouncer at the nightclub told officers that Spencer had offered to pay for it to stay open past the 3 a.m. closing time set by law and after being told no tried to punch the bouncer, a police report said.
Spencer’s agent, Roosevelt Barnes, did not immediately return a call Monday from The Associated Press seeking comment.
Cowboys spokesman Rich Dalrymple said the team was aware of the arrest but would not comment further until it learned more about what happened.
Spencer, 6-foot-3 and 257 pounds, was the Cowboys’ first round draft pick in 2007. He played at Purdue and is from Fort Wayne, Ind.
He had 34 tackles and two sacks for the Cowboys this season.