The arrest caused the Arizona Cardinals to release Floyd on Wednesday. The 27-year-old was found unconscious behind the wheel of a running vehicle at an intersection.
The Patriots need a receiver with Danny Amendola (ankle) ailing and decided to take a chance on Floyd.
Floyd, a five-year veteran, struggled with the Cardinals this season with 33 receptions for 446 yards and four touchdowns. His best season came in 2013 when he caught 65 passes for 1,041 yards.
Arizona teammate Larry Fitzgerald was supportive of Floyd after his release, and he told the team website on Thursday that he fielded calls from coaches and general managers seeking information about Floyd.
"I told them my honest opinion of him, that I think he'll be a great pickup for whoever," Fitzgerald said. "You've got a young guy who is hungry, who is eager to make plays in a contract year, has a chip on his shoulder now -- not that he didn't already have one -- and I hope he makes a big playoff run."
The Patriots opened up the roster spot by releasing receiver Griff Whalen, who had joined the team on Dec. 9.
Meanwhile, the Patriots worked out veteran return specialist Devin Hester on Thursday. Hester was released by the Baltimore Ravens on Tuesday, one day after making some decision-making gaffes on punt returns in a game against New England.
Hester, 34, holds the league record of 19 return scores. He has returned 14 punts for touchdowns and five kickoffs for scores.