Wow, that's a lot of negatives in the first few replies. But I'm glad some positives are joining in as well. Also, I cannot vote on your poll since the only options are "absolutely" and "don't be ridiculous" when I'd vote something like "it's conceivable but iffy."
After seeing characters like Data (Star Trek: The Next Generation) and the Doctor (Star Trek Voyager), Kryten (Red Dwarf), and even the Teenage Mutant Ninja Turtles, I spent a lot of time on this question back when I was a teenager. I even started to write a fanfic in which the Turtles get faced with "believe on the Lord Jesus Christ and you shall be saved" (boy was that a weird thought)! But I finally came to this general conclusion:
Assuming souls exist (which I do, based on the decades of research that have shaped my entire worldview), then I believe them to be the reason we can even contemplate questions like "do I have a soul?" With that idea as a starting point, I think that if a non-human creature (robot, alien, super-advanced animal) could get to the point of actually wondering that, he/she/it would have a soul.
But I think it's more likely that a robot would be able to mimic life enough to ask that, rather than honestly wondering for itself, which stays in the realm of soulless.
As for where the soul comes from, my worldview says "directly from God at the point of first breath," so I don't have a concrete idea of how these things get souls. I also sorta believe that God's plan for creation is going to conclude well before things get that complicated.
P.S. Go check out the webcomic Freefall for an overview of robots developing soul-consciousness. It's interesting.
ETA: A brief scan of posts above this says "soul" might need a definition.
Whether or not it exists, we as humans have a clear idea of a thing that is "me" that can be taken out of the body and put somewhere apart from the body (e.g., in another body) without losing any of the "me"-ness. Without this idea, stories such as the body-swapping in Stargate SG-1 would make no sense.
The soul concept is also that part that remains "me" even though time, disease (Alzheimer's), or injury (see Phineas Gage) may mess with my memory and personality to such an extent that people say I'm "a whole nother person" or not really myself.
If it helps, consider if a river is still the same river despite the entirety of its water being long gone, with new water in its place.