Integrated photonic circuits provide a versatile toolbox of functionalities for advanced quantum optics applications. Here, we demonstrate an essential component of such a system in the form of a Purcell enhanced single-photon source based on a quantum dot coupled to a robust on-chip integrated resonator. For that, we develop GaAs monolithic ring cavities based on distributed Bragg reflector ridge waveguides.Under resonant excitation conditions, we observe an over twofold spontaneous emission rate enhancement using Purcell effect and gain a full coherent optical control of a QDtwo-level system via Rabi oscillations. Furthermore, we demonstrate an on-demand 1 single-photon generation with strongly suppressed multi-photon emission probability as low as 1% and two-photon interference with visibility up to 95%. This integrated single-photon source can be readily scaled up, promising a realistic pathway for scalable on-chip linear optical quantum simulation, quantum computation and quantum networks.