If Ai became a reality and self-aware, able-bodied robots akin to humans were commonplace, would it be pious to convert the AI's to Judaism? Essentially, if a non-human wants to become Jewish, can we allow him?
I dont think it would be appropriate. The Talmud (Shabbat 88b) relates that when Moshe Rabbeinu went up to Heaven to receive the Torah, the angels protested: they wanted it for themselves. With the help of G-d, Moshe challenged the angels on several points relevant to our case, most notably:
What else is written in it? The Holy One, Blessed be He, said to him: “Honor your father and your mother” (Exodus 20:12). Moses asked the angels: Do you have a father or a mother that would render the commandment to honor them relevant to you?
Even if an AI was created to somehow procreate, feel jealousy, have arms and feet etc, there would inevitably be some small detail in which their experience differs from the human experience. Bottom line, the Torah was given for Man. Not for angels, not for AI, and probably not for aliens either.
Not sure what they would do about religion. They would need some sort of religion. Perhaps they could become Noahides, which is universal enough that it's conceivable many extraterrestrial societies would be able to find meaning in it. Or perhaps they would have already had a prophetic experience. Rabbi J.B. Soloveitchik is quoted in "The Rav Thinking Aloud" to believe in the possibility of an extraterrestrial "am hanivchar", which would imply a separate prophecy.
The assumption your making is just that - an assumption. Many technologists do not believe that AI can ever truly have a 'soul', as described by John Searle's Chinese room argument. Meaning a simulation of something is never the thing itself - AI inherently cannot be a human being despite it's amazing ability to replicate it. And machine learning exists, at the point it potentially ellipses human intelligence it will have morphed into something non-human. Furthermore the point at which human intelligence and computer intelligence are equal will be extremely short - artificial intelligence will grow at a much more rapid pace than pure human intelligence. In my opinion will will fuse with AI - similar to how our iPhones are a natural extension of our biological selves, therefore we will be the AI - and thus we will be AI Yidden.
This is an interesting subject on which there has been much debate. I was chatting with a rabbi about this on Facebook yesterday. I shared with him two essays that deal with the topic of kosher bots.
Here is a brief summary, in my words, of what the author wrote.
The author argues that there is no such thing as a "Jewish look." The concept is racist and antisemitic. Anyone could be Jewish or properly convert. There are black Jews, Asian Jews, ginger Jews, and white Jews, for example. It then seems reasonable enough that there may someday be a bot Jew with a bot mitzvah!
Later, the author makes the point that since some patriarchs were “pre-circumcised,” (ie Adam and Moses) it is not inconceivable that a Jewdroid can be “pre-circumcised,” or a female, without the requirement of circumcision. It can join a minyan, if male. Scientists argue that someday robots will surpass humans in intelligence and be very smart (more on this later). They will also be less likely, if at all, able to make mistakes and thus be good candidates for writing perfect Torah scrolls or leading the community as community rabbis.
As for the Jewish mother, the author argues that this tradition did not begin till the Mishnaic Period. Some rabbis argue that one’s Israelite identity goes by one’s father’s lineage according to the Bible. The author also argues that those who believe in evolution can accept that Jews descended from animals, and therefore, anyone could be a Jew. In fact, he argues that humans may not be the pinnacle of creation given that other species existed longer than humans.
Towards the end of the essay, he brings up the verse with Genesis, all humans are created in the “image of G-d.” He mentions the approach that early Israelites viewed G-d in anthropomorphic terms. If so, then Jewbots would also have G-d's "imagine." The author also argues for a more sophisticated version of this. Rambam, among others, felt that the "image of G-d" denotes intelligence. Since robots will possibly be more intelligent than humans someday.
Lastly, he shows two views from different rabbis and extols the former. If you are interested beyond reading my brief summary, and if you would like to see more content of the author, Roger Price is very knowledgeable and an interesting writer with ideas that make us think. You can visit his site here for more thought-provoking essays.
 The views summarized here are those of the author and do not necessarily reflect the views of the answerer
 Reform Jews also accept patrilineality descent