We study tunnel junctions consisting of a two-dimensional ferroelectric material sandwiched between graphene electrodes. We formulate a theory for the interplay of the polarization and induced free charges in such devices, taking into account quantum capacitance effects. We predict a gate-sensitive voltage difference across the polar domains, which can be measured using electrostatic force microscopy. Incorporating this electrostatic theory in the tunneling current-voltage characteristics, we identify a resonance peak associated with aligned Dirac cones as a highly sensitive probe of the polarization. This opens the way for device applications with few atom-thick polar layers acting as readable ultra-high-density memory.