Welcome to our interactive platform and thank you for contributing to it with your question!
There is a "U.S. Department of State" website about statelessness in general, stating it is impossible for those who are stateless to access many public "activities" - marriage included - as no legal protection from a state applies.
In order to get married, a passport is a core requirement. That means it is necessary to see if you will be granted Turkish citizenship. If you do, marrying should not be a problem. There is a visa that allows you to bring your fiance to the U.S. to get married, have a look here: https://travel.state.gov/content/travel/en/us-visas/immigrate/family-immigration/immigrant-visa-for-a-spouse-or-fiance-of-a-us-citizen.html
Also, here is a website that explains marriage laws in the U.S. - bear in mind that they change depending on which state you are in:
"Because state marriage laws in this area have been changing rapidly — many states have recently eliminated blood tests and or physical exams. You should check with your county marriage license bureau office, county clerk’s, city clerk’s, or town clerk’s office before making any wedding or travel plans."
I hope these sources help. Feel free to reach out to us again if you have any more questions!
All the best,