With the emergence and continued spread of the SARS-CoV-2 virus, and of the associated disease, coronavirus disease 2019 (COVID-19), there is an urgent need for improved understanding of how the body mounts an immune response to the virus. Here, we developed a competitive SARS-CoV-2 serological assay that can simultaneously determine whether an individual has developed antibodies against the SARS-CoV-2 Spike protein receptor-binding domain (RBD) and measure the proportion of these antibodies that block interaction with the human angiotensin-converting enzyme 2 (ACE2) required for viral entry. Using this assay and 144 SARS-CoV-2 patient serum samples, we found that a majority of anti-RBD antibodies compete for ACE2 binding. These results not only highlight the need to design vaccines to generate such blocking antibodies but also demonstrate the utility of this assay to rapidly screen patient sera for potentially neutralizing antibodies.