Polarization-sensitive (PS) terahertz (THz) technology can be used for investigating anisotropic materials that are opaque for visible light. A full characterization of an anisotropic material requires the extraction of the birefringence as well as the orientation of the optical axis from the measurement data. We present an approach based on THz time-domain spectroscopy (TDS) that exploits the spectral content of the THz signal for determining these two parameters from only two measurements. In contrast to an earlier approach with a more sophisticated PS-THz system and quasi-circularly polarized THz radiation, now a simple standard THz-TDS system can be employed. After a description of the mathematical model for data analysis we demonstrate the applicability of our method for a lithium niobate crystal and furthermore for a glass-fiber reinforced polymer sample, for which the orientation of the optical axis and birefringence are obtained in a spatially resolved way, showing the potential of the method also for PS-THz imaging. As no specialized setup or components are required, our approach can be easily and extensively applied for the analysis of anisotropic samples at THz frequencies.