The 26-year-old quarterback signed a two-year deal with the Raiders in March after spending the previous five seasons with the Tennessee Titans.
Irving last played in 2018 and was indefinitely suspended by the NFL in 2019 after violating the league's substance abuse policy. He was reinstated earlier in October.
The league's new collective bargaining agreement states that two practice squad members can be promoted to the active roster each week. The elevated players can then be returned to the practice squad without needing to go through waivers twice per season.
The Raiders brought in the lineman for a workout shortly after his reinstatement, and he could help bolster their pass rush.
Las Vegas has struggled to get consistent pressure this season, recording just seven sacks thus far. Pass-rusher Maxx Crosby is currently the only player with more than one sack.
Irving will reunite with defensive line coach Rod Marinelli. The two previously spent time together in Dallas.
The defensive lineman set a career high in sacks in 2017 with seven and has tallied 12.5 since entering the NFL.