The precision spherical joint is a key movement execution unit in robotics and in equipment with a parallel mechanism. When it works in passive motion, its arbitrary rotation angle cannot be determined. On the basis of the theory of equivalent magnetic charge, a measurement method through the installation of a ring permanent magnet (PM) and several Hall sensors was proposed. Firstly, the measurement model is developed on the basis of the theory of the permanent magnetic field model and the theory of equivalent magnetic charge. Then, a measurement prototype system is designed and developed; at the same time, a special data acquisition and process system is established to match the prototype. To test the sensor performance and its accuracy, an angle-comparing measurement and calibration device were developed. Experimental data show that in the ±15° cone space, the rod rotation angle can be determined steadily and the measurement accuracy can reach 1 min. With further study, expansion of the measurement range and improvement of the accuracy and resolution can hopefully be achieved. The sensor and method will have wide application prospects in the near future.