Extracting behavioral models of RRAM devices is challenging due to their unique “memory” behaviors and rapid developments, for which well-established modeling frameworks and systematic parameter extraction processes are not available. In this work, we propose a physics-informed recurrent neural network (PiRNN) methodology to generate behavioral models of RRAM devices from practical measurement/simulation data. The proposed framework can faithfully capture the evolution of internal state and its impacts on the output. A series of modifications informed by the RRAM device physics are proposed to enhance the modeling capabilities. The integration strategy of Verilog-A equivalent circuits, is also developed for compatibility with existing general-purpose circuit simulators. The Verilog-A model can be easily adopted into the SPICE-type simulator for the circuit design with a variable step that differs from the training process. Numerical experiments with real RRAM devices data demonstrate the feasibility and advantages of the proposed methodology.