Bigby, who started all 11 games, was hurt in the first half Sunday in a 16-13 overtime loss to Baltimore.
Bird played in nine games with the Chargers in 2011 after making the squad as an undrafted rookie from Texas Tech. He was released during final roster cuts in August.
The Chargers also filled a vacancy on their practice squad by signing safety Sean Cattouse, an undrafted rookie from California.
Also Tuesday, it appeared the Chargers are headed for their second straight local TV blackout and third this season. The team says nearly 12,000 tickets need to be sold by 1:25 p.m. Thursday or the game will be blacked out in Southern California.