Using first-principles calculations, we investigate the effect of tube size on optical properties of the zigzag, armchair, and chiral SiC nanotubes. The results indicate that the optical spectra of SiC nanotubes are dependent on the diameter and chirality, and that optical anisotropy is observed for different light polarizations. For a given chirality of SiCNTs, redshifts or blueshifts of the peaks in the dielectric function and energy loss function with increasing tube diameter are possible due to the competition between the size effect and pi orbitals overlapping, and the shifts become smaller as the tube diameter increases. The unusual optical properties of semiconducting SiC nanotubes present an opportunity for applications in electro-optical devices.