Barton is a rookie from Ohio State. He suffered a high ankle sprain in practice Thursday.
Barton was a seventh-round draft choice by Chicago and played in the Bears' season opener at Indianapolis. Following stints on the rosters of Miami and San Francisco, he was signed by the Bengals on Nov. 28 from the Miami practice squad.
Johnson originally signed with Cincinnati as an undrafted free agent from Kansas State on May 2. He played in all four preseason games, with 94 yards rushing on 21 carries and two receptions for 10 yards. He was waived on Aug. 30 and had been on the practice squad since then.