It is same as “Where do you wear your part?”. However, I don’t think it’s same as “Where do you arrange your hair?” Do you think they have the same meaning? Arrange seems to have a broader meaning than part here. I mean a part on the head is just one of arrangements you do on your hair. What do you think?
“Where do you part your hair?” is specifically asking where on their head someone makes a “parting”. A “parting” is the place where the hair separates, falling in one direction on one side of the parting, and the other direction on the other side, as in this picture:
“Where do you wear your part?” is not right. You could say “Where do you wear your parting?” though. “Where do you arrange your hair?” is more likely to produce an answer like “in my bedroom”, for example. If you want to ask about hairstyles you would say “How do you arrange your hair?”