Cincinnati placed sixth-round RB Rodney Anderson on the non-football injury list.
Smith, 32, is a former first-round pick of the Bengals back in 2009. After seven years in Cincinnati, Smith signed a one-year, $3.5 million contract with the Vikings in 2016 but lasted just a year in Minnesota.
Smith later returned to the Bengals on a one-year, $3.25 million contract before agreeing to a two-year, $8 million deal with the Cardinals in 2018.
The Cardinals elected to waive Smith halfway through the 2018 season, after which he re-signed with the Bengals.
In 2018, Smith appeared in eight games for the Cardinals and three games for the Bengals.