Prohibit Expansion of U.S. Combat Troops into Syria Act This bill prohibits the obligation or expenditure of Department of Defense funds for the purpose of: deploying members of the Armed Forces to Syria to engage in ground combat operations; awarding a contract to a private security contractor to conduct any activity on the ground of Syria; or otherwise establishing or maintaining any presence of members of the Armed Forces or private security contractors on the ground of Syria, unless the purpose of such presence is limited solely to rescuing or protecting members of the Armed Forces from imminent danger. The prohibition does not apply to the deployment of the Armed Forces to protect, rescue, or remove U.S. personnel.