Brown, 32, played for the Chargers during the 2012-13 seasons. He appeared in 30 games with one start, carrying the ball 91 times in the regular season for 377 yards (4.1 yards per carry) and a touchdown. Brown also totaled 57 catches for 431 yards (7.6 yards per catch).
Brown spent time with the Houston Texans earlier this season, appearing in three games. But Brown was released by the Texans last week.
To make room for Brown, the Chargers waived linebacker Kevin Reddick.
According to ESPN NFL Insider Field Yates, the Chargers also worked out running backs Brennan Clay and Cierre Wood on Tuesday.
Brown adds depth at the running back position, providing insurance should incumbent Donald Brown not return from a concussion suffered against the New York Jets last week. Ryan Mathews also remains out with a MCL knee sprain, so San Diego's healthy running backs included just Branden Oliver and Shaun Draughn.
The Chargers also officially placed center Doug Legursky on the season-ending injured reserve list with a knee injury. San Diego filled his spot by signing center Trevor Richardson off of the Cincinnati Bengals' practice squad to the team's active roster.