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, 40th overall (own)
3rd round, 71st overall (own)
4th round, 104th overall (own)
5th round, 134th overall (own)
7th round, 200nd overall (own)
The NFL will award compensatory picks after potentially the third, fourth, fifth, and sixth (and seventh rounds), so the picks in the fourth and later rounds will in all probability end up being later than they are currently listed. The Titans will probably receive at least one compensatory pick. I will update the exact pick numbers when that information is released.
The Titans currently hold six of their seven original selections, having traded away their sixth-round pick, 167th overall to the Minnesota Vikings for the 211th overall pick in the 2012 draft, which they used to select DE Scott Solomon. They have not acquired any picks from other teams.
When there are updates to the Titans' picks, I will update this post.