We have investigated the absorption of 0.9-1.4 nm silicon carbide nanoparticles (SiC NPs) by time-dependent density functional calculations, focusing on the effect of various oxygen adsorbates of the surface. We have found that Si-O and C-O single bonds result in relatively large optical gaps in the ultraviolet region while Si=O and C=O double bonds will dramatically lower the optical gap into the visible blue and red regions, respectively. Our findings can help interpret recent experiments on colloidal SiC NPs and their utilization in biological applications.