The ALPS Collaboration runs a “light shining through a wall” (LSW) experiment to search for photon oscillations into “weakly interacting sub-eV particles” (WISPs) inside of a superconducting HERA dipole magnet at the site of DESY. In this paper we report on the first successful integration of a large-scale optical resonant cavity to boost the available power for WISP production in this type of experiments. The key elements are a frequency tunable narrow line-width continuous wave laser acting as the primary light source and an electronic feed-back control loop to stabilize the power build-up. We describe and characterize our apparatus and demonstrate the data analysis procedures on the basis of a brief exemplary run.