With the regular season just concluded, the NFL has yet to officially determine the 2013 NFL draft order, but as far as I can tell the Tennessee Titans currently hold the following selections in the 2013 NFL entry draft:
1st round, 10th overall (own)
2nd round, 34th overall (via trade)
3rd round, 70st overall (own)
3rd round, 97th overall (compensatory)
4th round, 107th overall (own)
5th round, 142th overall (own)
6th round, 202nd overall (compensatory)
7th round, 248th overall (compensatory)
The Titans currently hold four of their seven original selections, having traded away their sixth-round pick, 166th overall, to the Minnesota Vikings for the 211th overall pick in the 2012 draft, which they used to select DE Scott Solomon and on the second day of the draft, and their second-round pick, 40th overall, and seventh-round pick, 216th overall, plus a 2014 third-round pick to the San Francisco 49ers for the 34th pick.
The Titans were also awarded three compensatory picks, in the third, sixth, and seventh rounds.
When there are updates to the Titans' picks, I will update this post.
UPDATE (2013/02/21): NFL released the official draft order, updated numbers.
UPDATE (2013/03/18): Compensatory picks announced. Updated accordingly.
UPDATE (2013/04/26): Second-round trade added.