Cook was with the Browns earlier this year before he was waived on May 21. The 5-foot-9, 210-pounder is the second-leading career rusher in Youngstown State history.
In the past few days, the Browns lost Lewis to a broken leg and Hardesty underwent knee surgery. Lewis is scheduled to have an operation to repair the fibula he broke Thursday night against Detroit. He could be lost for the season.
Hardesty is expected to be sidelined for at least one month.