A theoretical study of the ScCn, SCCn(+), and ScCn- (n = 1-10) cyclic clusters has been carried out employing the B3LYP density functional method. Predictions for several molecular properties that could help in their possible experimental characterization, such as equilibrium geometries, electronic structures, dipole moments, and vibrational frequencies, are reported. All ScCn cyclic clusters are predicted to have doublet ground states. For cationic clusters the ground state is alternate between singlets (n-even species) and triplets (n-odd members). In the case of anionic clusters the singlet-triplet separation is relatively small, with the singlets being favored in most cases. In general, even-odd parity effects are also observed for different properties, such as incremental binding energies, ionization energies, and electron affinities. For all neutral, cationic, and anionic clusters it is found that cyclic species are more stable than their open-chain counterparts. Therefore, cyclic structures are the most interesting possible targets for an experimental search of scandium-doped carbon clusters.