We present a graphene photodetector for telecom applications based on a silicon photonic crystal defect waveguide. The photonic structure is used to confine the propagating light in a narrow region in the graphene layer to enhance light-matter interaction. Additionally, it is utilized as split-gate electrode to create a pn-junction in the vicinity of the optical absorption region. The photonic crystal defect waveguide allows for optimal photo-thermoelectric conversion of the occurring temperature profile in graphene into a photovoltage due to additional silicon slabs on both sides of the waveguide, enhancing the device response as compared to a conventional slot waveguide design. A photoresponsivity of 4.7 V/W and a (setup-limited) electrical bandwidth of 18 GHz are achieved. Under a moderate bias of 0.4 V we obtain a photoconductive responsivity of 0.17 A/W.