Ray tracing accelerated with graphics processing units (GPUs) is an accurate and efficient simulation technique of wireless communication channels. In this paper, we extend a GPU-accelerated ray tracer (RT) to support the effects of reconfigurable intelligent surfaces (RISs). To evaluate the electric field, we derived a RIS path loss model that can be integrated into a RT and enables further extensions for the implementation of additional features and incorporation into complex reflective scenarios. We verify the derivation and implementation of our model by comparison with empirical measurements in a lab environment. We demonstrate the capabilities of our model to support higher-order reflections from the RIS to the receiver. We find that such components have a significant effect on the received signal strength, concluding that the extensions of advanced functionality enabled by our model play an important role in the accurate modeling of radio wave propagation in an environment including RISs.