Burnett, 25, originally signed with the Raiders as an undrafted free agent out of Nevada in 2012. He appeared in 22 games for Oakland between 2012-2013.
Burnett was signed to the Cardinals practice squad in October.
The Titans recently waived LB Shaun Phillips, who recorded only two sacks this season after signing with Tennessee this offseason. The linebacking corps was further depleted when the Titans elected to trade LB Akeem Ayers to New England for a late round draft pick.
Burnett will be counted on for special teams duty, but could see the field in the base defense considering the lack of depth.