It sounds doubtful, particularly if you use a conservative interpretation of Article I Section 9 of the Constitution. Part of the reason the nobility clause was added was to prevent "foreign influence", so "original intent" types will not be fond of this. Using a constitutional convention POD would pretty much be cheating, so maybe we need a closet Anglophile president for this to work. If the POD is too late, the current system of stuff like the Medal of Honor is already in place.
This is a difficult challenge.
I don't want to scream "Alien Space Bats!" like too many of our posters here, so let's find out. A variant John Adams presidency maybe could work? He suggested "His Highness" as a title for the president. . .
In 1810, however, a proposed amendment would have stripped citizenship from anyone receiving a foreign title. They did NOT want their republic to have any trappings of monarchy.
*Has thoroughly ransacked Wikipedia for information*