Brinkley, 30, is a former fifth-round pick of the Vikings. He spent the first five years of his career in Minnesota before he signed on with the Cardinals as a free back in March of 2013.
The Cowboys elected to sign him to a two-year, $6.5 million contract that included $2 million guaranteed back in March. However, he was released on Monday.
Last year, Brinkley appeared in all 16 games for the Vikings in 2014 and recorded 75 tackles, one sack and a forced fumble. Pro Football Focus has him rated as the No. 16 inside linebacker out of 60 qualifying players.