Fight for the American Dream Act This bill authorizes an individual to enlist in the Armed Forces if that individual has employment authorization under the Deferred Action for Childhood Arrivals program. (The program, often referred to as DACA, allows certain individuals without lawful immigration status and who arrived in the United States as children to temporarily remain in the United States, subject to various requirements and limitations.) An individual who has enlisted in the Armed Forces under this bill shall receive lawful permanent resident status, if the individual is otherwise eligible for such status. The bill waives certain grounds of inadmissibility related to unlawful entry for such individuals. If such an individual receives a discharge from the Armed Forces that is not an honorable discharge before completing a period of obligated service, the Department of Homeland Security must rescind that individual's lawful permanent resident status.