Can you put apple juice in the microwave?

Yes you can, it is often heated to make mulled cider. Originally a red hot wrought iron Poker [a mulling iron] was inserted into the mug to heat the cider. Mulled [hot] cider is often made with a few spices (cinnamon, nutmeg, cloves) and fruit (Oranges, cherries, raisins) added to "hard" [fermented] cider, and then heated to near boiling but not boiled. Some recipes today use sweet cider and add rum or Bourbon rather than using hard cider.