Has the USA ever had a monarch on their currency?

No.

The closest was currency issued by Hawaii, but the US Congress demonetized any Hawaiian coins in 1903 after Hawaii was annexed.

The United States has had Native American Chiefs on various coins, including Iron Tail (Lakota), Two Moons (Cheyenne) and John Big Tree (Seneca).

The colonies would have used British currency while they were colonies although people might have gotten letters of credit from a specific bank if they needed that. Those were not currency though, more like a check.

The U.S.A. never had a monarch. When there was a monarch over us, we weren’t the U.S.A. Our money depicts our own national figures, not those of another nation.

From the U.S. Treasury:

“The law prohibits portraits of living persons from appearing on Government Securities. Therefore, the portraits on our currency notes are of deceased persons whose places in history the American people know well.”