Not really sure about asperger's - I think it's more extreme and consistent lack of social skills.
Certainly, poor people skills is a potential symptom of SA, although I don't know in what context you find yourself "offending" people. One thing that people with SA may try to do in order to appear less boring to others is to try too hard to appear as gregarious, and then say stupid things.
Also, if it's just an occassional ill-judged remark, most people are guilty of that from time to time. Nobody's perfect.