Two separate injuries have limited Costa to only three games this season. The three-year pro strained his lower back in the team's opener against the New York Giants and sat out the next three weeks, then returned for Dallas' Oct. 14 matchup at Baltimore and started twice before hurting his right ankle in a Week 7 victory at Carolina.
Signed by the Cowboys as an undrafted free agent in 2010, Costa started all 16 games for the club last season.
To fill the available roster spot, Dallas signed rookie offensive tackle Darrion Weems off the Denver Broncos' practice squad.
