Jones was released by Dallas on Saturday as the team promoted defensive back Donovan Olumba from their practice squad.
The NFL waiver process runs from the day after the Super Bowl through the end of the regular season. With the postseason now set to begin, Jones will not officially be assigned to the Jaguars until after the conclusion of the playoffs.
Jones has appeared in 35 career games for the Cowboys and Green Bay Packers. He started 12 games for Green Bay over the previous two seasons while recording 126 tackles with three sacks, seven passes defended and one interception.
Jones appeared in six games for Dallas this season with almost all of his time spent on special teams.