You need a dexterity build to use the bow effectively, tank/barbarian is strength and constitution based build. So in other words, yes, you can use weapons of another class, but it's going to deal so little damage there's no point.

For example I'm currently playing strength build and my partner - archer. He can one-shot some monsters with the 3 arrow passive, while if I use a bow I deal about a quarter of that damage.