Tailored photonics cavities enhance light-matter interactions, ultimately enabling a fully coherent quantum interface. Here, we report an integrated microdisk cavity containing self-assembled quantum dots to coherently route photons between different access waveguides. We measure a Purcell factor of F-exp = 6.9 +/- 0.9 for a cavity quality factor of about 10,000, allowing us to observe clear signatures of coherent scattering of photons by the quantum dots. We show how this integrated system can coherently reroute photons between the drop and bus ports and how this routing is controlled by detuning the quantum dot and resonator or through the strength of the excitation beam, where a critical photon number less than one photon per lifetime is required. We discuss the strengths and limitations of this approach, focusing on how the coherent scattering and single-photon nonlinearity can be used to increase the efficiency of quantum devices such as routers or Bell-state analyzers.