Cognitive radio (CR) has become an important solution to address the spectrum shortage problems. However, CR networks are vulnerable to radio jamming attacks due to the open nature of wireless communication, making CR security a critical research focus. In this paper, we propose a reactive jamming resilient power allocation scheme that maximizes the communication rate of the secondary user (SU) against reactive jamming. Unlike existing anti-jamming schemes, our approach considers a stochastic jamming model and optimizes the SU’s transmit power to avoid the detection by the jammer. We first establish a CR network model incorporating time-varying channel gains and stochastic jamming behaviors, then leverage hypothesis testing theory to derive the adaptive optimal energy detection threshold for the jammer. To deal with the dynamic uncertainty of channel gains and jamming behaviors, we utilize a deep reinforcement learning-based solution, which enables the SU to learn the characteristics of the environment and adaptively optimize its strategies. Experimental results demonstrate that our scheme achieves a high communication rate while maintaining resilience against reactive jamming, highlighting its effectiveness in the dynamic CR networks.