Pullard, who is in his fourth season, was with the team during the preseason before being released. He played in 13 games and made 10 starts for the Chargers last season, with 47 tackles and an interception.
Badgley has made all three of his field-goal attempts and is 7 of 7 on extra points in two games after Caleb Sturgis was unable to kick due to a quadriceps injury. Coach Anthony Lynn said Monday that Sturgis has recovered from the injury.
The Chargers (5-2) have won four straight games and are at Seattle on Sunday.