Radio Galaxies (radio-loud AGNs, or RGs) are common in galaxy cluster media (ICMs). In addition to their potential thermodynamical roles, these RGs may also serve to illuminate important ICM dynamical features, especially ICM shocks. Those interactions are revealed most clearly by radio synchrotron emissions from associated RG Cosmic Ray Electrons (CRe). Here we report results from "MHD+CR" simulations of RG-shock encounters and specifically on resultant shock acceleration (DSA) of the CRe and observable consequences. We find, in particular, that even modest-strength ICM shocks (M_s \sim 3-4) may lead to significant and observable DSA of the RG CRe. This work has impact on both the nature of large scale cluster radio emissions, including so-called radio relics and our understanding of RG-ICM-shock dynamics.