can a us citizen become a citizen of another country
U.S. citizens are required by federal law to identify themselves with a U.S. passport, not with any other foreign passport, when entering or leaving the United States. The Supreme Court case of Afroyim v. Rusk declared that a U.S. citizen did not lose his citizenship by voting in an election in a foreign country, or by acquiring foreign citizenship, if they did not intend to lose U.S. citizenship. U.S. citizens who have dual citizenship do not lose their United States citizenship unless they renounce it officially.
Citizenship of the United States