We present a practicable way to take advantage of the spectral information contained in a broadband terahertz pulse for the determination of birefringence and orientation of the optical axis in a glass fiber reinforced polymer with a single measurement. Our setup employs circularly polarized terahertz waves and a polarization-sensitive detector to measure both components of the electromagnetic field simultaneously. The anisotropic optical parameters are obtained from an analysis of the phase and frequency resolved components of the terahertz field. This method shows a high tolerance against the skew of the detection axes and is also independent of a reference measurement.