As of now, the Bengals have three defensive tackles under contract; Domata Peko, Jason Shirley and Pat Sims. John Thornton is an Unrestricted Free Agent and Orien Harris is an Exclusive-Rights Free Agent. Harris, a 2006 fourth-round pick by the Pittsburgh Steelers, joined the Bengals before the regular season off waivers and played 14 games, started once, recording somewhere between 14 (NFL.com) and 22 tackles (Bengals.com). Harris has been a career practice-squad player before joining Cincinnati.
As it stands, the Bengals will start Pat Sims and Domata Peko with Jason Shirley rotating in. There's the high probability that the Bengals will bring John Thornton back to continue mentoring the younger tackles, as well as keeping his solid character in the lockerroom -- I wouldn't have any problem with that. It would also limit the issue of depth on defensive tackle to the point of picking a player in response to injuries.
On the other hand, Sims and Peko can't play every day, and Jason Shirley is a very green unproven commodity -- no matter how big Iggy's man-crush on him is. I kid. If the Bengals choose not to sign Harris, and Thornton signs elsewhere, then the Bengals will need to dig into free agency, if not the draft, to build back-end depth. Maybe a one-and-done type of role, or perhaps looking for needle-in-the-haystack talent in the run-of-the-mill rounds. Whatever. We project, using our guessing like a mofo with a basic understanding of the team's visions, personnel and historical processes, that the Bengals will need one more defensive tackle with the expectation that either Thornton or Harris do not return. And yes, I'm well aware that Jonathan Fanene has played defensive tackle; however that's typically in nickel formations.
Based on stats on Bengals.com
All that said, it wouldn't make sense for the Bengals to draft a defensive tackle in the first round, with Sims, Peko and Shirley all figuring into the team's long-term vision. We just need a late-round pick and/or a veteran defensive tackle, hoping that Thornton is up for that role again.