The coronavirus disease 2019 (COVID-19) pandemic, caused by infection with the severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2), is having a deleterious impact on health services and the global economy, highlighting the urgent need for an effective vaccine. Such a vaccine would need to rapidly confer protection after one or two doses and would need to be manufactured using components suitable for scale up. Here, we developed an Alphavirus-derived replicon RNA vaccine candidate, repRNA-CoV2S, encoding the SARS-CoV-2 spike (S) protein. The RNA replicons were formulated with lipid inorganic nanoparticles (LIONs) that were designed to enhance vaccine stability, delivery, and immunogenicity. We show that a single intramuscular injection of the LION/repRNA-CoV2S vaccine in mice elicited robust production of anti-SARS-CoV-2 S protein IgG antibody isotypes indicative of a type 1 T helper cell response. A prime/boost regimen induced potent T cell responses in mice including antigen-specific responses in the lung and spleen. Prime-only immunization of aged (17 months old) mice induced smaller immune responses compared to young mice, but this difference was abrogated by booster immunization. In nonhuman primates, prime-only immunization in one intramuscular injection site or prime/boost immunizations in five intramuscular injection sites elicited modest T cell responses and robust antibody responses. The antibody responses persisted for at least 70 days and neutralized SARS-CoV-2 at titers comparable to those in human serum samples collected from individuals convalescing from COVID-19. These data support further development of LION/repRNA-CoV2S as a vaccine candidate for prophylactic protection against SARS-CoV-2 infection.