In this paper, a scheme for coupling free-space THz radiation into a nonlinear whispering-gallery mode (WGM) resonator is presented. The purpose is to detect the weak THz radiation from the cosmic microwave background (CMB) by up-converting the signal into the optical domain via the nonlinearity of the medium. Such high-sensitivity receiver has theoretically shown capabilities towards photon counting at room temperature, however, it is critical to efficiently couple the THz radiation into the resonator. Therefore, by using the Schelkunoff-Waterman method (the so called T-matrix method) we perform an analytical evaluation of two different free-space coupling techniques: a frees-pace Gaussian beam, and a Gaussian beam incident in a silicon lens under total internal reflection. By comparing the excited modes in the resonator, the optimal parameters for each case are given.