in wow can a mage use a shield?

Answer 1

No, mages cant use shields. Only paladins, warriors and shamans can use shields.

Answer 2

Mages don't have the ability to physically wield a shield. Fortunately they have Mana Shield (absorbs damage at the cost of mana drained), Ice Barrier (very strong, powerful shield that absorbs almost 20,000 damage at 85) and Fire and Ice ward, which can be used to negate damage from the respective type.