We describe a fibre-based variable-incidence angle (VIA) polarization-sensitive swept-source optical coherence tomography (PS-SS-OCT) system to determine the 3D optical axis of birefringent biological tissues. Single-plane VIA-PS-OCT is also explored which requires measurement of the absolute fast-axis orientation. A state-of-the-art PS-SS-OCT system with some improvements both in hardware and software was used to determine the apparent optical birefringence of equine tendon for a number of different illumination directions. Polar and azimuthal angles of cut equine tendon were produced by the VIA method and compared with the nominal values. A quarter waveplate (QWP) and equine tendon were used as test targets to validate the fast-axis measurements using the system. Polar and azimuthal angles of cut equine tendon broadly agreed with the expected values within about 8% of the nominal values. A theoretical and experimental analysis of the effect of the sample arm fibre on determination of optical axis orientation using a proposed definition based on the orientation of the eigenpolarization ellipse experimentally confirms that this algorithm only works correctly for special settings of the sample arm fibre. A proposed algorithm based on the angle between Stokes vectors on the Poincaré sphere is confirmed to work for all settings of the sample arm fibre. A calibration procedure is proposed to remove the sign ambiguity of the measured orientation and was confirmed experimentally by using the QWP.