Is there a specific arc for Sinon in the anime?
The whole Phantom Bullet arc is Sinon's arc, in the same way the Fairy Dance is mostly Leafa's arc, for the most part. Neither character has another side-story outside of these arcs, seeing as most of their past is expanded within them.

In the Light Novels, this is Volumes 5 and 6. Most of what you want to know about Shino/Sinon will be in those two volumes.