Well, how does anyone become an actor? Talent, and opportunity.
I imagine it's the same, whether you're an Aspie, or NT.
That being said, there are some advantages, and disadvantages an actor with AS would have, compared to a neurotypical actor.
For example, a person with AS must become a student of human behavior, out of necessity. "Becoming a character," comes easily to people with AS, due to a lifetime of practice. The downside of this, is that such behavior can appear disingenuous, or robotic. To a neurotypical, normal behavior comes naturally. However, because their own behaviors are so reflexive, NT's are generally uncomfortable, "stepping into someone else's shoes," for a role.
That's my hypothesis. 