As someone with Asperger's, I'm going to take a contrary view to A.P.'s answer.
Wikipedia mentions that Aspie is used amongst sufferers:
People identifying with Asperger syndrome may refer to themselves in casual conversation as aspies (a term first used in print by Liane Holliday Willey in 1999).
Oxford Dictionaries has a number of examples as well; however none of their examples includes any context, particularly on whether they refer to self-description.
Whether a term is derogatory or not depends a great deal on context. As with any nickname or slang term which highlights a physical feature, it is usually Not OK to use it of others: cf. "Carrot-top", "Fatso", "Four-eyes" and the like — along with other more polarising epithets. Each of these might be used affectionately if one knows the person concerned well enough, particularly if they use the term themselves to self-describe. However to call someone who wears glasses "Four-eyes" without knowing whether they use the term themselves is quite likely to be derogatory.
Thus it's likely to be fine to use the term of someone who self-describes as Aspie, but it is less likely to be acceptable when used by non-sufferers of those whom they do not know will not object.
[As you might guess from this answer, I object.]
