The technique of resonant ultrasound spectroscopy was used to measure the elastic properties of a polycrystalline cubic silicon carbide (3C-SiC) thin film. The film, grown on a silicon (100) substrate, was 1.69 microns thick with columnar crystalline grains and a (111) texture. The substrate with the film was placed between two transducers and the resonant frequencies were measured; measurements were repeated after selective, timed dry etching of the film, allowing a determination of the elastic constants of the film alone. The film elastic constants, c(11)=371 and c(12)=146 GPa, were within a few percent of the literature values (c(11)=386, c(12)=136 GPa) of crystalline 3C-SiC. However, the film elastic constant c(44), 111 GPa, was significantly smaller than the bulk literature value, 254 GPa. For the film, c44 approximately (c(11)-c(12))/2, indicating that, quite unlike a bulk 3C-SiC crystal, the thin film is elastically isotropic.