Standard empirical atom-atom potentials are shown to be unable to describe the binding of PAH molecules in the variety of configurations seen in clusters. The main reason for this inadequacy is the lack of anisotropy in these potentials. We have constructed an anisotropic atom-atom intermolecular potential for the benzene molecule from first principles using SAPT(DFT) interaction energy calculations and the Williams-Stone-Misquitta method for obtaining molecular properties in distributed form. Using this potential as a starting point we have constructed a transferable anisotropic potential to model intermolecular interactions between polycyclic aromatic hydrocarbons (PAH). This new potential has been shown to accurately predict interaction energies for a variety of dimer configurations for four different PAH molecules including certain configurations which are poorly predicted with current isotropic potentials. It is intended that this potential will form the basis for further work on the aggregation of PAHs.