From Article I, Section 9 of the US Constitution:
“No Title of Nobility shall be granted by the United States: And no Person holding any Office of Profit or Trust under them, shall, without the Consent of the Congress, accept of any present, Emolument, Office, or Title, of any kind whatever, from any King, Prince, or foreign State. “
... assuming anyone pays attention to it anymore.
A sham Nobel Peace Prize while barely in office set a preceden regarding Article 1 Section 9.