In the document, the two countries' "close cooperation" and "common interests" are mentioned.
"The USA will regard any armed attack on the state of Qatar's territory, sovereignty or critical infrastructure as a threat to the USA's peace and security", it says, among other things.
The USA also promises to "guarantee the security and territorial integrity of the state of Qatar against external attacks".
The document, according to the news agency AP, is dated Monday, but was made public on Wednesday. It is unclear what the president's promises of defense would mean in practice.
In September, Israel attacked a building complex in Qatar's capital Doha, which is said to have caused irritation with the American government. The USA is at the same time a close ally of Israel.
Trump, who, among other things, has received a luxury plane as a gift from the Qatari regime, has several times spoken well of the country's leadership. The USA also has, among other things, a military base in Qatar.
