In Munchkin, Can a Wizard use his charm ability when he has no cards to discard in the hand?
No he can't, although official evidence is a little circumstantial. This question is in an old version of the Munchkin FAQ (but not the current one):
This is corroborated on the Munchkin wiki:
As was already stated in the other answers, discarding an empty hand is not possible.
This clarification is missing in the new Munchkin FAQ, because the wizard cards' text changed in the newer editions. The changelog summarizes:
This means with the old rules you need at least one card, with the new rules at least three cards for the Charm spell.