ヅラ here means かつら, I think, but the translation of the whole sentence could vary, depending on the context.

Let's say the person uttering this sentence is A and the other person is B.
If this sentence follows B telling a story about what he said about A to someone else, then it could be "That makes it sound like I wear a wig!"

Alternatively, it could be that A is looking at a picture of himself (and possibly other people) in which his hair looks unnatural, then he could be saying to B, "I look like I'm wearing a wig, don't I!?"

Or even something else...hard to tell without context.