I don't know if it's common or not, but I would guess that it isn't uncommon, because one of the core pieces of ASDs is difficulty with aspects of socializing. If a person has difficulty in social situations, it seems logically more likely that said person would develop anxiety related to social situations because of feeling pressured, confused, overwhelmed, rejected, etc. (I just picked examples from my own experience that led to my social anxiety.....I don't actually know how most people--AS folk or not--experience social interaction emotionally....I'd be interested in others' responses!) Ongoing discomfort or bad experiences related to socializing seems like it could set the stage for anxiety.
There is help for it, there's therapy if you can access it, and self-help books. I don't much more than that because I've not managed to deal with my own social anxiety yet.