We study the impact of gas motions on the polarization of bright X-ray emission lines from the hot intercluster medium (ICM). The polarization naturally arises from the resonant scattering of the emission lines owing to a quadrupole component in the radiation field produced by a centrally peaked gas-density distribution. If differential gas motions are present in the cluster then the line can leave the resonance, affecting both the degree and the direction of polarization. The changes in the polarization signal are, in particular, sensitive to the gas motions perpendicular to the line of sight. We calculate the expected degree of polarization for several patterns of gas motions, including a slow inflow expected in the simplest version of a cooling flow model and a fast outflow in an expanding spherical shock wave. In both cases the effect of nonzero gas velocities is found to be minor. We also calculate the polarization signal for a set of clusters, taken from large-scale structure simulations, and evaluate the impact of the gas bulk motions on the polarization signal. We argue that the expected degree of polarization is within reach of the next generation of space X-ray polarimeters.