The topological structure associated with the branch point singularity around an exceptional point (EP) can provide tools for controlling the propagation of light. Through use of graphene-based devices, we demonstrate the emergence of EPs in an electrically controlled interaction between light and a collection of organic molecules in the terahertz regime at room temperature. We show that the intensity and phase of terahertz pulses can be controlled by a gate voltage, which drives the device across the EP. Our electrically tunable system allows reconstruction of the Riemann surface associated with the complex energy landscape and provides topological control of light by tuning the loss imbalance and frequency detuning of interacting modes. Our approach provides a platform for developing topological optoelectronics and studying the manifestations of EP physics in light–matter interactions.