What is your goal???????
To bring her to the US as your wife? Or just marry in the US as Thais and live in Thailand?
If you plan to marry in the US and live in the US in hopes of getting a green card, then you need to apply for a visa for your girl friend.
I "believe" if you apply for a different type of visa, say tourist for the U.S. with the purpose of being married to apply for a green card that is breaking one of their rules!!!! Now that you have discussed this on a public platform I would never swear to the fact you were just vacationing and got caught up in the moment and got married.
There are CLEAR rules on this, consulting the US Government website is an excellent place to get official information and keep you out of trouble later.
Best of luck! Chok Dee!