The 264-pound Hartsock, who had only three catches and was essentially another lineman for Atlanta's powerful running game, injured a toe in last weekend's 45-28 victory over Carolina. He is out for the season after making eight starts in 11 games.
"It's going to be tough to replace Ben," coach Mike Smith said. "Ben has done a very nice job in blocking. He's an integral part of our running game."
Rader was released by the Falcons after training camp, then re-signed and actually started in a loss to Philadelphia, only to get cut again.
Justin Peelle, who has nine catches for 99 yards this season, will likely move into the starting role for Sunday's game at San Diego, with Rader taking over the backup role.