Orr played for Houston and Jacksonville last season. The 6-foot-1, 246-pounder will give the Browns depth and fill a spot opened when outside linebacker Chaun Thompson signed a two-year contract last week with the Houston Texans.
The 26-year-old Orr began last season with the Texans and made two starts before being waived after six games. He was signed by the Jaguars in December and played in three games.
Orr entered the NFL as an undrafted rookie free agent out of Michigan in 2003. He had his best season in 2005, when he made 12 starts and recorded a career-high seven sacks.