The dense environment of a galaxy cluster can radically transform the content of in-falling galaxies. Recent observations have found a significant population of active galactic nuclei (AGN) within jellyfish galaxies, galaxies with trailing tails of gas and stars that indicate significant ram pressure stripping. The relationship between AGN and ram pressure stripping is not well understood. In this letter, we investigate the connection between AGN activity and ram pressure in a fully cosmological setting for the first time using the RomulusC simulation, one of the highest resolution simulations of a galaxy cluster to date. We find unambiguous morphological evidence for ram pressure stripping. For lower mass galaxies (with stellar masses < 10^9.5 solar masses) both star formation and black hole accretion are suppressed by ram pressure before they reach pericenter, whereas for more massive galaxies accretion onto the black hole is enhanced during pericentric passage. Our analysis also indicates that as long as the galaxy retains gas, AGN with higher Eddington ratios are more likely to be the found in galaxies experiencing higher ram pressure. We conclude that prior to quenching star formation, ram pressure triggers enhanced accretion onto the black hole, which then produces heating and outflows due to AGN feedback. AGN feedback may in turn serve to aid in the quenching of star formation in tandem with ram pressure.