The pet form of Anca is Ancuta. The name Ana doesn't have any relation with the name Anca, they are two different names. The name Ana is also used with Maria (the romanian form of Mary) to form Anamaria or a French version Anne-Marie.
It is not a diminutive of Ana, at least not in Romanian. Both Ana and Anca have a common origin (Hebrew), and their own diminutives in Romanian. The one for Anca is Ancuța (pronounced Ankutzah).