Preventive Care Awareness Act of 2021 This bill requires the Department of Health and Human Services (HHS) to promote the use of preventive health care services. In particular, HHS must focus on decreasing disparities in accessing preventive services for individuals in rural and underserved communities who delayed or forewent recommended preventive services during the COVID-19 pandemic. Specifically, HHS must carry out a campaign to increase public awareness about and use of recommended preventive services. HHS must also convene a task force to develop recommendations regarding preventive services during and after the COVID-19 pandemic and future pandemics. The recommendations must address, among other considerations, reducing disparities in health outcomes and identifying barriers to implementing the recommendations. Additionally, the Centers for Disease Control and Prevention must provide grants to states, tribes and providers of tribal health services, territories, and localities for increasing patient uptake of recommended preventive services.