The Titans currently have Charlie Whitehurst in place as their No. 2 quarterback and rookie Zach Mettenberger behind him.
Davis, 24, signed with the Falcons as an undrafted free agent out of Boston College back in 2012. He appeared in just one game for Atlanta completing five of his seven pass attempts for 34 yards.
Atlanta placed him on waivers back in June, but he did work out for the Patriots in recent weeks.