Can a us citizen marry a foreign national on a tourist visa?

Yes, even two non-citizens with visas can get married. Just bring your visa and passport to the county courthouse and register for a lisense.

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You can get married, but you cant have the status of the non-immigrant adjusted if you get married in the USA without going through the proper K1 Visa process.

Here is information on how to obtain a K1 Fiancee Visa

http://fianceek1visa.blogspot.com/

www.visajourney.com