You can. VAC bans do not affect other games other than those they are issued for.

However:
While VAC and game bans (in most cases) do not affect other games, some server admins of custom servers intentionally ban players that have VAC or game bans in other games from their custom servers because they deem such players to not be trustworthy. Nobody wants to play with cheaters, rule violaters or gullible players that allow others to cheat or break rules on their behalf.

引用自 Невпустоте：

Can I play Dota if I got vac-banned in Counter-Strike 2?

1 VAC ban on record | Info
535 day(s) since last ban

only affects the game what you banned in.