The coherent exciton dynamics in molecular complexes composed of ring-shaped aggregates induced by linear- and circular-polarized laser fields has been investigated by using the quantum master equation (QME) approach. As shown in previous studies, near-degenerate states create the superposition states after irradiation of linear-polarized laser fields and thus cause the oscillatory exciton recurrence motion. In contrast, the rotatory exciton recurrence motion is found to be induced by circular-polarized laser field in a C3-symmetry complex composed of identical three ring-shaped aggregates. This exciton dynamics is predicted to originate in the superposition states between the two pairs of degenerate states, which are coherently excited by a circular-polarized laser field. The rotatory exciton recurrence motion induced by a two-mode laser field with mutually opposite circular polarizations also has been examined in the complex composed of two different-sized groups of ring-shaped aggregates. It turns out that the two-mode laser field induces mutually counter-rotatory exciton recurrence motions concurrently, which are generated separately on the two different groups of ring-shaped aggregates. These results suggest the possibility of controlling rotatory exciton recurrence motions by using the circular-polarized laser fields and ring-shaped aggregate complexes.