Draughn, 27, signed an exclusive rights tender back in March with the Browns, but was unfortunately among their final roster cuts at the start of the season.
Cleveland later added him to their practice squad, only to promote him to their active roster after they traded DL Billy Winn to the Colts in return for a conditional 2017 seventh-round pick.
However, the Browns wound up releasing Draughn a few weeks ago.
In 2014, Draughn appeared in 11 games for the Browns and ran for 19 yards on 10 carries (1.7 YPC) and no touchdowns. He also contributed 173 kick return yards.