We study the effects of rotation on the dynamics, energetics, and super(56)Ni production of pair instability supernova (PISN) explosions by performing rotating two-dimensional ("2.5D") hydrodynamics simulations. We calculate the evolution of eight low-metallicity (Z = 10 super(-3), 10 super(-4) Z sub(middot in circle)) massive (135-245 M sub(middot in circle)) PISN progenitors with initial surface rotational velocities of 50% of the critical Keplerian value using the stellar evolution code MESA. We allow for both the inclusion and the omission of the effects of magnetic fields in the angular momentum transport and in chemical mixing, resulting in slowly rotating and rapidly rotating final carbon-oxygen cores, respectively. Increased rotation for carbon-oxygen cores of the same mass and chemical stratification leads to less energetic PISN explosions that produce smaller amounts of super(56)Ni due to the effect of the angular momentum barrier that develops and slows the dynamical collapse. We find a non-monotonic dependence of super(56)Ni production on rotational velocity in situations when smoother composition gradients form at the outer edge of the rotating cores. In these cases, the PISN energetics are determined by the competition of two factors: the extent of chemical mixing in the outer layers of the core due to the effects of rotation in the progenitor evolution and the development of angular momentum support against collapse. Our 2.5D PISN simulations with rotation are the first presented in the literature. They reveal hydrodynamic instabilities in several regions of the exploding star and increased explosion asymmetries with higher core rotational velocity.