Davis, who arrived recently after being let go by the Colts, was added to the active roster on Saturday.
The Bengals will also be without cornerback Trae Waynes, who is out with a hamstring injury.
Davis, a second-round pick of the Steelers, played his first four years in Pittsburgh. He has spent time since then with Washington, Pittsburgh, Indianapolis, and now the Bengals.
The 1-0 Bengals have a chance to get to 2-0 in the top-heavy AFC North, and possibly to prove that their division is the best one, top to bottom, in the league.