The signing Friday leaves the Bengals with five of their eight picks under contract.
Bodine is only the third player in franchise history who was acquired through a trade to move up in a round. The Bengals swapped two picks with Seattle for the chance to get Bodine, who will have a chance to win the starting job. Veteran center Kyle Cook was released in the offseason.
Cincinnati also has signed quarterback A.J. McCarron (fifth round), linebacker Marquis Flowers (sixth round), receiver James Wright (seventh round) and cornerback Lavelle Westbrooks (seventh round).
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