The anisotropic detection technology of crystals is gradually developing towards non-contact and non-destructive methods. Terahertz radiation has broad prospects in studying birefringence of anisotropic materials due to its large penetration depth and non-ionization characteristics for many dielectric materials. Quartz, sapphire, liquid crystal, and metamaterials containing sub-wavelength structures exhibit terahertz birefringence. As a common material in polarization functional devices, the parameter measurement is of great significance for developing terahertz devices. The extraction of material birefringence often depends on previous knowledge, such as optical axis direction and crystal thickness. The materials optical axis direction characterizes its anisotropys preferred direction. The appropriate Jones vector can be selected according to experience for crystals with known optical axis orientation. In practical applications, only the terahertz waves linear polarization direction, optical axis, and detection axis can be selected. It is easy to measure the ordinary and extraordinary light and calculate their refractive index directly from the time domain signal. For materials with unknown optical axis direction, it is necessary to rotate the sample to measure in different orientations. In addition, the extraction of birefringence depends on the thickness of the materials. The measured value obtained by vernier caliper or micrometer is quite different from the true value, and it is easy to cause scratches on the samples surface. At the same time, whether it is sample rotating or thickness measurement, human operation will introduce uncertainty for birefringence characterization. Based on the Terahertz time-domain spectroscopy (THz-TDS), a non-contact measurement method for the optical axis direction and the thickness of the birefringent crystal is developed in this paper. The complete refractive index properties of the crystal can be obtained without relying on the crystals prior parameters.The automatic positioning of the optical axis is realized by controlling the rotation of the sample and the action of the optical delay line. The iterative approximation algorithm of the transfer function is used to extract the crystal thickness and complete refractive index information.To validate our method, the (10-10) oriented sapphire, which exhibits birefringence at terahertz frequencies, was selected. We extracted the average extraordinary and ordinary refractive indices of sapphire in the frequency range of 0.3～1.5 THz, which is 3.08±0.02 and 3.39±0.02, respectively. The birefringence is -0.31±0.02, and the absorption spectrum was plotted. The results show that our method avoids sample damage and positioning errorscaused by manual operation and improves the efficiency, stability, and accuracy of terahertz birefringence extraction. It is significant to the polarization-sensitive terahertz measurement technology and its application.