The monkey paw is an item on the Odd Old Man's list during the Rag and Bone Man I quest. It is dropped by monkeys. The bone must be put into a pot of vinegar and boiled to create a polished monkey paw before giving it to the Odd Old Man.
After the polished monkey paw is given to the Odd Old Man you can no longer obtain this as a drop but it is possible to receive multiple items prior to turning in the cleaned bone.
For an exhaustive list of all known sources for this item, see here