Yes, Ferric chloride can be used to etch stainless steel. In the field of chemical etching, one of the most popularly used etchants is Ferric chloride.
Ordinarily, ferric chloride is usually mixed with water in equal proportions to create hydrochloric acid in the solution. Although, it is commonly used in steel etching, however, it can also be used to etch stainless steel. Compared to pure acid, it can also be used on a wide range of resist materials; albeit this may come with a consequence if not appropriately attended to — it can pit the surface.