A ben noach is not permitted to offer an animal missing a limb as a korban. Tosfos (A"Z 5a) asks why this issur is not counted among the 7 mitzvos bnei noach and answers that the 7 mitzvos bnei noach are all prohibitions; in this case the ben noach has a positive commandment to bring a kosher korban. (I believe I once before posted my wife's suggestion in a moment of Brisker genius: the 7 mitzvos are all issurei gavra; an animal missing a limb is an issur cheftza, and hence not counted.)
What exactly is the positive commandment obligating the ben noach to bring a kosher korban? The Mishna laMelech (Hil Melachim 10:7) concludes from here that a ben noach is included in the commandment of bal yacheil... kol hayotzei m'piv ya'aseh, the command to fulfill one's pledges. The Yerushalmi (Nazir 9:1) debates whether a ben noach can have a vow absolved by a chacham, also implying as well that a ben noach's vows and pledges are binding. The Ml"M is incomfortable with his these, as the parsha of vows and pledges seems to have been given only to the Jewish people, but he does not offer an alternate answer.
The Avnei Miluim (1:2) suggests another way out. The halacha is "amiraso l'gavoha k'mesiraso l'hedyot", a pledge to the mikdash is like a finalized sale. Failing to deliver a korban is like failing to deliver goods after selling them to a vendor -- it is no different than theft, one of the seven ben noach laws.
The Ml"M makes another an interesting point. Even if keeping nedarim are not obligatory for a ben noach, it does seem from simply reading chumash that a ben noach must keep a shevu'ah. We find numerous examples in Sefer Braishis of shevous being made: Avraham asks Eliezer to take a shevu'ah, Avraham swears to Avimelech, etc. One could argue that the Avos kept the Torah and went above and beyond the requirement of other bnei noach, but that theory does not resolve every example he gives.