The laser-polarization effects on nonadiabatically couple pi-electron rotation (ring current) and molecular vibration have been theoretically analyzed for aromatic molecules with quasi-degenerate excited states irradiated by an ultrashort laser pulse of arbitrary polarization. We first derived general formulations of the coherent electronic wave packet and expectation value of electronic angular momentum within a frozen-nuclei model. The relative quantum phase of the superposed quasi-degenerate States, which.. determines the oscillating behavior of angular momentum; can be manipulated by the ellipticity and orientation of the incident laser. Nuclear wave packet simulations with a model molecule confirmed the controllability of pi-electron rotation, although the angular momentum is gradually reduced by nonadiabatic couplings. The amplitude of molecular vibration depends prominently on the orientation of linear polarization vectors rather than the helicity of circular polarization. The characteristic feature in vibrational amplitudes is attributed to the interference in nonadiabatic transition governed by the-relative quantum phase between nuclear wave packets. This offers a new strategy for laser control of molecular vibrations through the wave packet interference in nonadiabatic transition.