We write down an effective theory of the Polyakov loop to investigate the deconfinement phase transition of imaginary-rotating gluonic matter using the strong-coupling expansion. We find the strength of the nearest-neighbor Polyakov-loop interaction modified by the sum of contributions involving the chair-type loops along the temporal direction. Our results show that the deconfinement transition temperature increases with increasing imaginary angular velocity, which agrees with the predictions from the models and the high-temperature perturbative calculations.