The Cardinals also placed OL Tarik Cole and RB Xavier Turner on waivers.
Pullard, 27, is a former seventh-round pick of the Browns back in 2015. He spent less than a year in Cleveland before he was waived and later signed to the Jaguars practice squad.
The Chargers claimed Pullard off of waivers in 2017 and he has been on and off of their active roster the past two years.
In 2018, Pullard appeared in nine games for the Chargers and recorded 17 tackles and no sacks.