Can I make wudu with a wig on?

Wiping the head is required

Wiping over the head is one of the obligatory parts of wudu, named in the Quran:

Scholars differ on how much of the head: the Shafi'is say any part is enough, the Hanafis say a quarter, and the Malikis and Hanbalis say the whole head. Either way, the wiping should reach your own hair or scalp when that's reasonably possible. See What are the obligatory parts of wudu?

Removable wigs and toppers

A wig on clips, combs or an adjustable band is like a hat: take it off, wipe your head with wet hands, and put it back after wudu. If you wear a wig cap or thin liner underneath, most scholars say wiping over it isn't enough; slip it back a little so your wet fingers touch your hair or scalp at the front. If you're in public, a quiet bathroom stall works well.

Bonded or glued hair systems

Some people, often men with hair loss or women after chemotherapy, wear units glued to the scalp for weeks. Removing them for every wudu would be impossible. Here scholars differ:

• Many contemporary scholars allow wiping over the unit, comparing it to wiping over a turban or a bandage. The Prophet ﷺ once wiped over his forelock and his turban in wudu (Sahih Muslim 274).
• Others say wiping must reach your real hair or scalp, so you should wipe whatever part of your own hair or scalp is exposed, such as the sides or back.

When the wig is for a medical reason, the case for ease is stronger. See also Can I make wudu with a cast or bandage?

A note on wearing wigs at all

Scholars also discuss whether wearing a wig or added hair is allowed in the first place, since a hadith strongly criticises adding hair to one's own. Views range from forbidding it to allowing it for illness or hair loss. That's a separate question from wudu. See Can I wear a wig instead of a hijab? For ghusl, which needs water on the scalp, see Can I do ghusl with hair extensions?