Cox, a fifth-round selection by Denver in the 2010 draft, started nine times as a rookie last year and recorded 58 tackles, one interception and 14 passes defensed. However, the talented youngster's future with the organization was placed in jeopardy following an arrest last December for allegedly raping am incapacitated woman at a suburban apartment complex.
The 24-year-old is scheduled to go on trial in October.
Denver also released veteran wide receiver David Anderson and tight end Dante Rosario, and placed cornerback Syd'Quan Thompson on injured reserve while waiving 21 other players to reach the final limit.
Anderson was signed by the Broncos just prior to training camp after a five- year stint with the Houston Texans in which the Colorado State product compiled 81 receptions and three touchdowns. His best season came in 2009, when he started eight games and caught 38 passes for 370 yards.
Rosario had spent the past four seasons playing under current Denver head coach John Fox in Carolina and had a career-best 32 catches for the Panthers in 2010.
Thompson, who tied for the Broncos' lead with two interceptions in 13 games last season, tore his Achilles' tendon in the team's preseason finale at Arizona on Thursday.
The Broncos also waived defensive end Jeremy Beal, cornerback Brandon Bing, linebackers Alvin Bowen and Lee Robinson, defensive tackles Ronnell Brown, Jeremy Jarmon and DeMario Pressley, guards Jeff Byers, Stanley Daniels and Eric Olsen, wide receivers Britt Davis, D'Andre Goodwin, Greg Orton and Eron Riley, offensive tackle Adam Grant, tight end Dan Gronkowski, kicker Steven Hauschka, running backs Jeremiah Johnson and Austin Sylvester, safety Kyle McCarthy and quarterback Adam Weber. In addition, running back Brandon Minor and wide receiver Jamel Hamler were placed on injured reserve.
Jarmon, a third-round choice by Washington in the 2009 supplemental draft, had been acquired by Denver in a trade for veteran wide receiver Jabar Gaffney on July 27. Beal was a seventh-round selection (247th overall) of the Broncos in this past April's draft out of the University of Oklahoma.