I just read last night in Unfamiliar Fishes that it was King David Kalakaua of Hawaii sometime in the 1870s.
We became a nation under the Constitution in March 1789.
The first monarch to visit the new country would have at that time, or within a month, with the annual northern migration of the Monarch Butterfly.
Whut?
Amusingly, the guest lived in the White House before his host did. As a small child, Harald was taken to England along with his parents and grandfather as the Nazis invaded. His mother brought him to America when she came for a visit, and FDR, finding her charming company, invited them to stay in White House guest rooms for a few months, which they did. He’s almost certainly the only reigning monarch who once lived in the White House.