No, they do not automatically become a U.S. Citizen. You must first file form I-130, Petition for Alien Relative to begin the process for your spouse to obtain permanent resident status. If they are legally present in the United States, they may be eligible to also file for Adjustment of Status with USCIS. If they are outside of the U.S. or do not qualify to file for Adjustment of Status, after USCIS approves the I-130 Petition, it is forwarded to the U.S. Department of State’s National Visa Center (NVC) for processing. Once NVC processing is complete, the case is sent to a U.S. Consulate in your spouse’s home country where the medical examination and interview will take place. After your spouse becomes a permanent resident, he or she will be eligible to file for Naturalization to U.S. Citizenship in three years if you are still married.