We report the first experimental measurement of the near-threshold photoionization spectra of polycyclic aromatic hydrocarbon clusters made of pyrene C16H10 and coronene C24H12, obtained using imaging photoelectron-photoion coincidence spectrometry with a VUV synchrotron beamline. The experimental results of the ionization energy are compared to calculated ones obtained from simulations using dedicated electronic structure treatment for large ionized molecular clusters. Experiment and theory consistently find a decrease of the ionization energy with cluster size. The inclusion of temperature effects in the simulations leads to a lowering of this energy and to quantitative agreement with the experiment. In the case of pyrene, both theory and experiment show a discontinuity in the IE trend for the hexamer. This work demonstrates the ability of the models to describe the electronic structure of PAH clusters and suggests that these species are ionized in astronomical environments where they are thought to be present.