Yes!
https://en.wikipedia.org/wiki/Lunar_Flag_Assembly

However, the US is a member of the Outer Space Treaty, so it can't claim celestial bodies.
https://en.wikipedia.org/wiki/Outer_Space_Treaty
Article II of the treaty explicitly forbids any government from "appropriating" a celestial body such as the Moon or a planet, whether by declaration, use, occupation, or "any other means".