Last season, Trent played in six games with the Bengals, one game with the Indianapolis Colts and five games with Jacksonville after being waived twice during the season.
According to a league source, the Detroit Lions also put in a competing waiver claim for Trent. However, the Redskins have a higher priority for waiver claims.
Torrence spent the past three seasons with the New Orleans Saints.
Last season with the Saints, he had 17 tackles, one interception, a sack, four pass deflections and eight special-teams tackles.
Torrence, 30, has 94 career tackles, two interceptions, 11 pass deflections and 3 1/2 sacks.
He has 61 special-teams tackles. Torrence went undrafted out of Stanford, signing with the Green Bay Packers before being released and signing with the Atlanta Falcons.
For more coverage of the NFL, go to profootball.scout.com.
Follow me on Twitter: @RavensInsider