Jobs to Fight COVID-19 Act of 2021 This bill requires the Department of Labor to award grants to states and other governmental and native American entities to (1) support the recruitment, placement, and training of—and provide employment to—certain individuals seeking employment in COVID-19 (i.e., coronavirus disease 2019) contact tracing and pandemic response positions; and (2) assist with the transition to new employment or education and training of these individuals in preparation for and upon termination of such employment. The employees must be paid at least the required prevailing wage and fringe benefit rates. In addition, the Centers for Disease Control and Prevention (CDC), in coordination with the Department of Health and Human Services and state, local, tribal, and territorial health departments, must establish and implement a national evidence-based system for COVID-19 testing, contact tracing, surveillance, containment, and mitigation. The CDC shall also award grants or contracts to these entities for such activities and to public entities to implement multilingual and culturally appropriate COVID-19 awareness campaigns.