The NFL has awarded all of the compensatory draft picks for the 2012 Draft, which means the draft order is officially complete. Compensatory picks only affect rounds 3 through 7.
The Cleveland Browns received four of compensatory picks. Here they are:
(Round/Pick/Overall)
6 35 204 Cleveland (Compensatory Selection)
6 36 205 Cleveland (Compensatory Selection)
7 38 245 Cleveland (Compensatory Selection)
7 40 247 Cleveland (Compensatory Selection)
The Browns' other draft picks are:
(Round/Pick/Overall)
1 4 4 Cleveland
1 22 22 Cleveland from Atlanta
2 5 37 Cleveland
3 4 67 Cleveland
4 5 100 Cleveland
4 23 118 Cleveland from Atlanta
5 4 139 Cleveland
5 25 160 Cleveland from Denver
7 4 211 Cleveland
Because of compensatory slots, the Browns have a few dense spots. They will draft back to back in the sixth round at Nos. 204 and 205, and in the seventh round they'll draft at Nos. 245 and 247.
Here is an article with a complete list of all NFL Draft picks, including compensatory picks.