We demonstrate the measurement of nanoparticle anisotropy by angularly resolved Rayleigh scattering of single optical levitated particles that are oriented in space via the trapping light in vacuum. This technique is applied to a range of particle geometries from perfect spherical nanodroplets to octahedral nanocrystals. We show that this method can resolve shape differences down to a few nanometers and be applied in both low-damping environments, as demonstrated here, and in traditional overdamped fluids used in optical tweezers.