Peru has begun opening up to some countries, but the United states is not part of those countries so far. Currently it looks like you can only fly into Peru from Santiago, Chile; Bogota, Colombia; Santa Cruz, Bolivia and Quito, Ecuador.
For those able to travel into Peru, passengers will be required to carry proof of a negative COVID-19 PCR test that was taken at most 72 hours prior to travel. Passengers must also complete a "Declaracion Jurada de Salud" at 72 hours before departure. All passengers will need to install and complete a "Pre Registro de Control Migratorio" on their personal device before departure. This will generate a QR code which must be presented upon arrival
***Update, as of November 2, 2020 ***
Passengers are now able to carry a negative Coronavirus (COVID-19) RT-PCR or antigen test result, or an epidemiological medical discharge certificate as proof they they do not have COVID-19.