A theoretical study of the MgCn, MgCn+, and MgCn- (n = 2-7) cyclic clusters has been carried out. Predictions for their electronic energies, rotational constants, dipole moments, and vibrational frequencies have been made at the B3LYP/6-311G(d) and B3LYP/6-311+G(d) levels. MgCn cyclic clusters generally have singlet ground states, whereas both cationic and anionic clusters have doublet ground states. An even-odd parity effect (n-even clusters being more stable than n-odd ones) is observed for both the neutral and anionic species, whereas in the case of the cations, there is no clear alternation in stability. Ionization potentials exhibit also a clear parity alternation trend, with n-even clusters having larger values than n-odd ones. In the case of electron affinities, initially the same behavior is observed, but for larger members the trend is reversed and n-odd compounds have higher electron affinity. It is also found that neutral clusters prefer cyclic structures over open-chain isomers, especially for high n. On the other hand open-chain ground states are predicted for both anionic and cationic clusters, except for the first members of the series.