Parker, 30, spent the last five seasons with the Chiefs before being released in March. He recorded 67 tackles and two interceptions in 2017.
A starter each of the last four seasons, Parker spent the early part of his career bouncing around rosters. He played for the Oakland Raiders, Carolina Panthers and Seattle Seahawks (on three separate occasions) in 2011 and 2012.
The Falcons are unlikely to offer Parker a chance to start. He's likely being brought in as insurance for Ricardo Allen, who is playing under a one-year contract after signing his restricted free-agent tender.
Allen and 2017 Pro Bowler Keanu Neal are slated to start, so Parker might not even be guaranteed to make the roster.