Molecular beam scattering measurements of total cross sections have been performed at a sufficiently low energy in the thermal range and at an angular resolution high enough to permit for the first time the observation of the "glory" interference effect in collisions of a benzene molecule with He, Ne, and Ar. Information on range, strength, and anisotropy of the interaction in the C6H6- rare gas dimers has been obtained from the analysis of the energy dependence of the total cross sections. In benzene-He, -Ne, and -Ar dimers bond energies are 0.98, 1.95, and 4.20 kJ/mol, respectively, for the most stable geometry, in all cases an out-of-plane configuration with the rare gas atom located on the 6-fold symmetry axis of benzene, at distances of 0.323, 0.331, and 0.359 nm, respectively. The results of the present investigation show that well depths for all three systems decrease by a factor 2 or 5 and corresponding distances increase by 40% or 70% for planar rare gas approaches respectively perpendicular to a C-C bond or collinear to a C-H bond (estimated uncertainties of 10% for bond energies and 3% for bond lengths). These experimental findings provide a crucial test of correlation formulas recently proposed (Chem. Phys. Lett. 2001, 350, 286-296) to estimate van der Waals minimum well depths and distances at selected approach geometries of rare gases on hydrocarbons.