Are there any medicines that can cure Asperger syndrome?

No. At present, no medications have been shown to treat any form of pervasive developmnental disorder (pdd)--increasing called autism spectrum disorders (asd). Some symptoms such as repetitive behaviors and obsessions may respond to medications, but we have no cure--or even good treatement--for the disorder itself, whether asperger's or autism .
Aspergers. There should never be a "cure" for asperger's. I find it to be a more highly evolved brain. Watch my explanation here. But there are downsides associated with rigidity, depression and anxiety, as well as irritability. There are medications which can help with those issues but i encourage my aspies to celebrate their strengths. Watch this.
No. Not at this time. There are various medications to address various symptoms or behaviors, but not cure the disease itself.