In this work, we derive a systematic and general CG parametrization method for anisotropic particles with a strong theoretical basis in rigorous statistical mechanical principles and develop a computer algorithm for implementing it. The method, which we have called anisotropic force-matching coarse-graining (AFM-CG), is a generalization to anisotropic CG particles of the multi-scale coarse-graining (MS-CG) method for isotropic CG particles, which uses force matching to relate interactions in the underlying FG model to those in the CG model. Unlike existing anisotropic force-matching methods, the AFM-CG method is developed to approximate the FG PMF in a finite-temperature, manybody condensed-phase system without assuming pair interactions between CG particles and is not limited to specific functional forms of the CG potentials, forces, or torques. As proofof-principle, the method is applied to systems of two anisotropic molecules, benzene and perylene. A number of structural, thermodynamic and dynamical properties are compared between the CG and FG models to verify the accuracy of the CG models and AFM-CG method.