Can a disabled person on SSI marry a non-US citizen?

Yes, a U.S. citizen may marry a foreign national regardless of whether the U.S. citizen may be disabled. Beyond that, upon becoming married, a U.S. citizen generally is able to sponsor a foreign national for immigration benefits through a marriage-based adjustment of status application (so that the foreign national may become a Lawful Permanent Resident - sometimes called "getting a Green Card." That is true regardless of whether the U.S. citizen may be disabled. Note, however, that if the U.S. citizen spouse does not have sufficient documentable income to meet the Affidavit of Support requirements, then it may be necessary to have a joint sponsor for the application. Generally any U.S. citizen or Permanent Resident who has sufficient documentable income and who is willing to assume the responsibilities contemplated in the Affidavit of Support may serve as a joint sponsor. Of course, there are many other details that determine immigration eligibility. It would be wise for you and your fiance/fiance to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.