When an individual is a legal citizen of two countries, it is known as having dual citizenship. While individual countries in the global system vary in the rules and regulations for permitting their citizens to hold multiple citizenship, the United States allows it. While it is not strictly required that a citizen give up his dual citizenship to join the U.S. military, it may be necessary to do so.
You do not actually have to be a citizen of the United States to join its military. Indeed, many immigrants use military service as a venue to improve their ability to make the transition from legal resident to full citizen. While historically the U.S. military has only been open to legal residents, individuals who hold documents known as "Green Cards" may have other options. In 2009, the military was considering a measure that would allow temporary immigrants, in the country legally, to join the military for an accelerated path to citizenship. Soldiers are not strictly required to renounce another citizenship to join the military.
Part of joining the military is a background check. Every member of the armed forces must be able to obtain at least a "confidential" rating, meaning that they can be trusted with sensitive, but not classified, information. If the job the dual citizen is applying for does not require a full security clearance at the "Secret" level, then this background check primarily involves talking to friends and family about the prospective recruit's moral character. As long as these interviews do not make it clear that the recruit's dual citizenship calls the recruit's loyalties to the United States into question, a dual citizenship is usually not a problem.
High Security Clearance
However, if the military job which the recruit is applying for requires a "Secret" security clearance level, a dual citizenship can be a serious obstacle. These are individuals who will be dealing with information that can harm United States interests if leaked into the wrong hands. Consequently, the investigation scrutinizes the potential recruit's background more closely. Depending on the job, the dual citizen might have to renounce his non-U.S. citizenship. It is also possible that the very existence of the alternate citizenship in the first place will disqualify him from getting a security clearance for a particular job.
Unlike enlisted personnel, officers in the United States military must be U.S. citizens and U.S. citizens alone. If an officer candidate has a dual citizenship, then he must renounce it in order to receive an officer's commission. Furthermore, all United States military officers must be able to receive a "Secret" security clearance level. Depending on the country from which the prospective officer candidate has his other citizenship, and his previous visitation and involvement with that country, the individual may be unable to receive a security clearance even if they are willing to renounce their foreign citizenship.