The presence of discontinuities can significantly weaken rock masses, whose shear load-bearing capacity is always dictated by discontinuity failures. The shear response of rock discontinuity has been extensively studied under low loading rate conditions, while the effect of impact loading on its shear strength was unclear. To address this issue, rock discontinuity samples with quantified surface roughness were tested under six normal stresses (0%, 5%, 10%, 15%, 20%, and 25% of its uniaxial compressive strength) and different loading rates (varying from 100 MPa/ms to 700 MPa/ms) by a novel-designed impact shear testing system. Experimental results show that the impact shear strength is proportional to the loading rate and exhibits significant rate dependence. Moreover, the cohesion is clearly rate-dependent and the friction angle keeps constant during impact loading, which shows obviously different behaviors with those under static loading conditions. Considering the rate effect of the shear strength parameters, the shear strength criterion of rough rock discontinuity under impact loading was established. Furthermore, a statistical constitutive model was proposed by incorporating the Weibull distribution of the shear damage. The successful application of the theoretical model to the experimental data shows that the proposed models can well predict the shear strength and describe the shear damage of rough rock discontinuities under impact loading.