Cook, a 5-9, 210-pound running back is in his rookie season out of Youngstown State, originally signed with the Browns as an undrafted free agent on April 30. He was waived May 21.
Cook finished second in Youngstown State history with 4,052 career rushing yards, while adding 39 touchdowns on 811 attempts. He totaled more than 1,200 rushing yards and at least 11 rushing scores in each of his three seasons as a starter.
A native of Middleburg Heights, Ohio, he graduated from Midpark High School.
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Cleveland and Cincinnati kick off at 1 p.m. Sunday