Pitts is a 6-1, 310-pound product of Louisiana Tech. In his final year in college, he had 53 tackles and 3.5 sacks.
Backup defensive tackles Jermaine Haley (shoulder) and Damian Gregory (knee) have both missed practice time because of injuries.
In another roster move on Wednesday, the Dolphins waived/injured cornerback Jeff Harris, a seventh-round pick in the 2000 draft.
Harris hasn't fully recovered from a severe knee injury that landed him on injured reserve last season.