Campbell played for Bengals offensive coordinator Hue Jackson when he was the Oakland Raiders' head coach.
He was recently cut by the Cleveland Browns.
Campbell passed for 11 touchdowns and eight interceptions with 2,015 yards and a quarterback rating of 76.9 last season as he started eight games.
For his career, Campbell, who has also played for the Washington Redskins, has passed for 16,697 yards, 87 touchdowns and 60 interceptions.
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Aaron Wilson covers the Ravens for The Baltimore Sun