Dynamic spectrum access (DSA) and simultaneously wireless information and power transfer (SWIPT) are two promising approaches to address the spectrum and energy supply problems. However, most existing works studied these two techniques separately, and how to effectively realize them simultaneously is non-trivial, because the power allocation of DSA and time splitting of SWIPT will influence both data transmission and energy harvesting performance. Hence, a sophisticated joint design is necessary, which, however, is challenging considering the uncertain dynamic spectrum environment. In this paper, we propose a joint power allocation and time splitting scheme to facilitate devices to implement both DSA and SWIPT simultaneously, which aims at maximizing the long-term throughput while ensuring the interference limitation and energy supply requirements. Considering the environmental uncertainty, we develop a multi-agent deep reinforcement learning solution to make each device autonomously select the best decision that could optimize the whole network performance based on its local observations. Simulation results have shown the effectiveness of the proposed scheme.