Moore was the Raiders' fifth-round pick in 2011. He played in 51 games and started 37 for Oakland, making 142 catches for 2,169 yards and 17 touchdowns. He also returned punts.
Last season, Moore played in 10 games - two as a starter - but caught only 12 passes for 115 yards.
The Bengals kept receiver Brandon Tate by signing their unrestricted free agent to a deal last week. Tate also returns punts and kickoffs.
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