I subscribe to the belief of anything living has a soul, and that life constitutes more than just a pulse or the flow of energy, and is hard to describe but easy to name. This fits in with my particular idea of the meaning of life to be the full formation of a soul, and then the shaping of it, which is where the idea of sentience comes into play.
To put it simply, there's a difference between an "advanced soul," which is the idea of a spirit, something that carries on thoughts and mindstructure, and a soul, or just a "spark of life." A spirit has a whole afterlife (which I truly haven't really delved into as much as I should have. All I've really come up with is that there's a form of Hell, be it oblivion, punishment, or just damnation, ie. in the absence of an omnipresent force. If there is a Heaven or opposite of Hell, I've yet to really focus on it), while an unformed spark can at most become part of new life. It's important to note that sentience only comes into the shaping process, not the forming (meaning nonsentient life may fully develop itself, but a sentient one can go on to shape what its spirit will eternally be like).
So if a robot is more than just a machine performing a simple task (and I mean something like just an arm here), than yes it has a soul. If it does not think however (doesn't have to think up complex ideas, it just has to be able to supply its own input such as finding a solution to its power source being low just like an animal has to do when they are hungry), it does not have a spirit.
This system is actually just as (un)fair to humans as it is to everything else I apply it to (so robot soul advocates who want to complain about how cruel it is for thinking robots that can't work outside of their programming should listen up), as it's rather harsh on people who die before their time, or who are raised wrong, or suffer brain injuries and don't die immediately.