The Falcons parted ways with former 2012 fifth-round pick Bradie Ewing a few weeks ago, so they could use some help at fullback.
Jones, 32, signed a one-year deal with the Texans last year after spending the first eight years of his career with the Jaguars.
Last year, he totaled two carries for one yard and caught five receptions for 34 yards receiving over the course of 16 games.
Pro Football Focus has Jones rated as the No. 9 fullback in the league last season.