Jones, 29, has played for the Dallas Cowboys (2004-07), Miami Dolphins (2008-09) and Denver Broncos (2010). After spending training camp with the Broncos this season, he re-signed with the Dolphins on Sept. 20, playing in two games before being released again Oct. 5.
He adds experience to the defensive backfield, having played in 101 career games (nine starts).
Jones, like fellow cornerback Devin McCourty, played at Rutgers. In addition to three career interceptions, Jones has recorded 59 special-teams tackles. He also saw time at safety with Denver last season.
The release of Adams, who played in 51 snaps on Sunday in Philadelphia, left the Patriots with only three cornerbacks before Jones' signing.
"We felt like we needed to make a roster move, so had to clear a spot there," coach Bill Belichick said of the move to cut ties with Adams, who does not have practice-squad eligibility.
Of the four cornerbacks on the roster, McCourty has missed the past two games with a shoulder injury, and Antwaun Molden left Sunday's contest with an undisclosed injury. In his place, rookie safety Sterling Moore saw time at cornerback, while wide receiver Julian Edelman played 16 snaps at the position.
Mike Rodak is a frequent contributor on Patriots coverage to ESPNBoston.com.