According to the Journal of Communication Disorders, Deaf Studies and Hearing Aids: Rethinking Asperger's: Understanding the DSM-5 Diagnosis by Introducing Sheldon Cooper:
The DSM-5 has revised criteria for the diagnosis of the developmental disorders. The DSM-5 has eliminated Asperger’s Disorder and created the umbrella title, Autism Spectrum Disorder (ASD). At Rutgers Robert Wood Johnson Medical School, residents in training learn about the latest revisions of the DSM through media. The character, Sheldon Cooper, from The Big Bang Theory meets criteria in the DSM-IV for Asperger’s Disorder. By assessing Sheldon’s behavior across several episodes, the viewer can reevaluate Sheldon considering the new criteria. When Sheldon Cooper is used as a model, a patient with a DSM-IV diagnosis of Asperger’s would now be diagnosed in the DSM-5 with ASD, level 1 severity, without accompanying intellectual impairment, without accompanying language impairment.
So, it is possible, were Sheldon to be diagnosed by a real-world clinician, he would be found with what was commonly referred to as Asperger's. However, in the TBBT universe, he is probably just odd.
After all, many otherwise intelligent and highly trained individuals, such as Leonard's mother, Dr. Beverly Hofstadter, Ph.D., M.D., didn't ever claim that Sheldon was special. Of course, the fact is that many of Sheldon's idiosyncrasies also exist in Dr. Hofstadter, so perhaps she isn't the best example I could give.
All in all, I think Penny best summed it all up when she asked Sheldon: "What is wrong with you?!"