The Outer Space Treaty, signed in 1967, prohibits it. It was first signed by the U.S., the U.K, and the Soviet Union. The treaty forms the basis of international space law. As of 2011, 100 countries have signed and ratified the treaty and another 26 have signed, but have not ratified it.
The treaty also prohibits any nation from placing a nuclear weapon or other weapon of mass destruction into orbit around Earth. Neither can any nation put one on the Moon or any other celestial body. The Moon is exclusively for peaceful purposes, too.