Skelton signed a day after the reigning NFC champions waived rookie B.J. Daniels, who still could be an option to join the practice squad if he clears waivers. The 25-year-old Skelton, hoping to catch on with a team for good in his fourth NFL season, completed 320 of 602 passes for 3,707 yards and 15 touchdowns in his three seasons with the Cardinals from 2010-12.
The Bengals have picked Josh Johnson as their backup quarterback.
Skelton was a fifth-round pick from Fordham in 2010 who started 17 games in three seasons, including six last year. He has completed 53 percent of his passes for 3,707 yards with 15 touchdowns and 25 interceptions.
Skelton beat out Kevin Kolb for the starting job under then-coach Ken Whisenhunt in training camp last season. He was hurt in the opener and Kolb took over.