We demonstrate the feasibility of fabricating light-waveguiding microstructures in bulk single-crystal diamond by means of direct ion implantation with a scanning microbeam, resulting in the modulation of the refractive index of the ion-beam damaged crystal. Direct evidence of waveguiding through such buried microchannels is obtained with a phase-shift micro-interferometric method allowing the study of the multimodal structure of the propagating electromagnetic field. The possibility of defining optical and photonic structures by direct ion writing opens a range of new possibilities in the design of quantum-optical devices in bulk single-crystal diamond.