We demonstrate a ring resonator for gigahertz surface acoustic waves (SAWs) consisting of a Ge waveguide on a silicon chip. SAWs generated by interdigital transducers on a section of the waveguide are guided over a curved path and detected by a second interdigital transducers. The structure of the GHz waveguide modes mapped using high resolution interferometry compares well with elastic calculations. The acoustic propagation properties as well as the potential applications of these semiconductor-based resonators are discussed.