Ah, Socrates supposes there that the soul is "like the divine" as opposed to the body which is like mortal things. He means that the soul is in the class of things that are unchanging, immutable, invisible, and grasped by the intellect rather than the senses, He doesn't say anything about the soul being a 'part of the gods'. And it doesn't sound like he's thinking of anything like the Prometheus myth, given the things he associates with the soul (ideal, invisible, immutable, etc.).
If you asked Plato about selling your soul, I think he would think you were just being silly.
If something was divine, then it was under the domain of the gods; I was making a simple extrapolation.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.