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The government website doesnβt say anything about any documents apart from a passport valid for 6 months.
I guess you should also have a good travel history and no criminal record in Jordan or anywhere in fact.
You should also have:
Proof of return
Adequate health insurance
Adequate finds
Intended address(es)
A passport with a validity of at least six months and a visa are required. Jordan issues single-entry visas to U.S. citizens upon arrival at Ammanβs Queen Alia International Airport, Sheikh Hussein crossing at the Israeli border, and the three border crossings with Saudi Arabia (Umari, Mudawara and Durra).
Note the visa will cost around $56.