My guess is that a neurologist would have to make the diagnosis, although I might be wrong?
I've worked with children who have autism, but not Aspergers children as much. If I suspected I myself had Aspergers traits I would see a specialist of some sort, because some of the Aspergers symptoms can be easily confused with other issues (depression, anxiety, social phobias, etc.). Aspergers has a large range of functionality/symptoms, etc.
Here's a quiz:
Aspie-quiz
By no means a diagnostic tool, but sort of interesting.