Williams played in five games with the Jets before being released. He was then claimed on waivers by the Texans, with whom he collected 12 tackles and one interception in 10 games.
The 27-year-old had a career-best six interceptions and 1.5 sacks with the Jets in 2015. He has recorded 107 tackles, 10 interceptions, 2.5 sacks, two forced fumbles and one fumble recovery in 49 career games with the Jets and Texans.
Williams is expected to add to the Cardinals' depth in a secondary that features Pro Bowl selection Patrick Peterson, Bene Benwikere, Brandon Williams, Lou Young III, Jonathan Moxey, C.J. Goodwin and Jarell Carter.