Yes all the big supermarkets stock soya milk and many other "health food" products (that's usually the section where you find soya milk).
You probably won't find it in the small corner supermarkets or "kiosks" as they are sometimes known as they only stock one or two cartons which are quickly sold, so head for the larger supermarkets such as Papantoniou, Orphanides, Carrefour or E and S to find what you need.
If eating out, make sure you ask the restaurant for the ingredients of any dish you are unsure of just to make sure they have not used any dairy products.
