The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) readily infects a variety of cell types impacting the function of vital organ systems, with particularly severe impact on respiratory function. It proves fatal for one percent of those infected. Neurological symptoms, which range in severity, accompany a significant proportion of COVID-19 cases, indicating a potential vulnerability of neural cell types. To assess whether human cortical cells can be directly infected by SARS-CoV-2, we utilized primary human cortical tissue and stem cell-derived cortical organoids. We find significant and predominant infection in cortical astrocytes in both primary and organoid cultures, with minimal infection of other cortical populations. Infected astrocytes had a corresponding increase in reactivity characteristics, growth factor signaling, and cellular stress. Although human cortical cells, including astrocytes, have minimal ACE2 expression, we find high levels of alternative coronavirus receptors in infected astrocytes, including DPP4 and CD147. Inhibition of DPP4 reduced infection and decreased expression of the cell stress marker, ARCN1. We find tropism of SARS-CoV-2 for human astrocytes mediated by DPP4, resulting in reactive gliosis-type injury.