Partial discharge (PD) refers to a physical phenomenon that local discharge occurs between two electrodes without forming a full connection or a bridge. Continuous PD activity can significantly shorten the lifespan of electrical equipment. Therefore, it is crucial to monitor and identify PD signals. Traditional methods for measuring PD signals are limited by the metal materials and size of the antennas used, making it difficult to achieve near field detection inside a equipment like switchgear in substations, which limits the improvement of measurement sensitivity. This paper proposes a novel method for measuring PD signals based on Rydberg atoms, which allows for in situ near-field high-sensitive non-metallic detection. In our experiment, one of the most common types of PD phenomenon, corona discharge, is selected for model preparation and measurement. Firstly, cesium atoms are excited to the Rydberg state by two-photon excitation, and then the corona discharge signals are measured based on AC-Stark effect of Rydberg atoms. Finally, the measurement results are analyzed using the phase-resolved partial discharge spectroscopy method, and the phase distribution characteristics of the corona discharge and the distribution of discharge pulses are obtained.