The adsorption of four aromatic hydrocarbon compounds, benzene, naphthalene, anthracene, and phenanthrene, at the surface of I_h ice is investigated by grand canonical Monte Carlo (GCMC) computer simulation under tropospheric conditions at 200 K. By systematic variation of the value of adsorbate chemical potential in the simulations, the adsorption isotherms are determined. It is found that adsorption follows the Langmuir mechanism only up to a rather low relative pressure value in every case. In this range specific surface sites, called α sites, to which adsorbate molecules can be bound particularly strongly in specific orientation, are occupied. In these α sites, presumably the dangling OH bonds of the ice surface form O–H^....π-type hydrogen bonds with the delocalized π electrons of the adsorbed aromatic molecule lying parallel with the ice surface. Once these α sites are saturated, lateral interactions become increasingly important, leading to large fluctuations of the lateral density of the adsorption layer and an increasing deviation of the adsorption isotherm from the Langmuir shape. The adsorption layer is found to be strictly monomolecular and even unsaturated in every case, as condensation well precedes the saturation of this monolayer for all four aromatic adsorbates considered in this study.