The team is exploring backup options, signifying a lack of confidence in Burrow's availability.
This move follows the Bengals' recent signing of veteran backup quarterback Reid Sinnett to their practice squad.
McCarron, known for his college football career at Alabama, last played for the St. Louis Battlehawks in the XFL, leading the league in touchdown passes.
He had previous NFL stints with the Bengals, Bills, Raiders, Texans, and Falcons.