The electrical anisotropy of rock is characterized by tensor resistivity. The four-pole method and six-pole method are mostly used to measure rock resistivity in the laboratory, but it is difficult to fill the nine components of tensor resistivity in one experiment. And multiple experiments are easy to cause large measurement errors. For this reason, based on the document Calculating Water Saturation in Electrically Anisotropic Media, this paper designs a conductivity tensor measuring instrument for square cores, which is also available for plunger cores. Nitrogen is used to displace a completely water-saturated core, and the temperature and pressure inside the core holder are controlled by a temperature control system and a confining pressure control system. The bridge instrument can control the electrode to measure the nine components of conductivity tensor at different water saturations. The instrument can also be used in rock-electric experiments to determine the unknown coefficients a, m, b, n in the Archie formula through the measured conductivity tensor data. The feasibility of the design of the conductivity tensor was verified by theoretical and experimental data analysis.