In this Letter, we present single-pixel spiral phase contrast imaging that enables optical edge detection of both amplitude and phase objects. This technique utilizes single-pixel detection to directly acquire the Fourier spectrum of the edge-enhanced object by scanning spiral phase-encoded plane waves in k-space. Experimentally, we exploit a digital micromirror device to simultaneously generate the plane wave and reference field for illuminating the object and scan the plane wave for spectrum sampling. During the process, four-step phase-shifting is adopted, and synchronized intensity measurements are made with a single-pixel detector. Applying an inverse Fourier transform to the obtained spectrum directly yields the edge information of objects. As a demonstration, digital and real objects are imaged, and results verify that isotropic edge detection can be achieved with our technique for both amplitude and phase objects.