The effects of the rotational degrees of freedom in the photodissociation dynamics of diatomic molecules by a chirped laser pulse is studied. In general, the inclusion of rotational degrees of freedom reduces the efficiency of the chirping excitations relative to that found for nonrotating molecules. However, using classical 2D and 3D rotating Morse oscillator models we demonstrate that field polarization can cause dramatic enhancements of the dissociation probabilities, with circularly polarized chirped pulses inducing dissociation in rotating molecules almost as efficiently as that previously seen for nonrotating Morse oscillators. We suggest reasons for such improvement in efficiency and discuss the validity of the bucket dynamics model for rotating Morse oscillators.