Optical beam steering has broad applications in lidar, optical communications, optical interconnects, and spatially resolved optical sensors. For high-speed applications, phased-array-based beam-steering methods are favored over mechanical methods, as they are unconstrained by inertia and can inherently operate at a higher speed. However, phased-array systems exhibit a tradeoff between angular range and beam divergence, making it difficult to achieve both a large steering angle and a narrow beam divergence. Here, we present a beam-steering method based on wavefront shaping through a disorder-engineered metasurface that circumvents this range-resolution tradeoff. We experimentally demonstrate that, through this technique, one can continuously steer an optical beam within a range of 160° (80° from normal incidence) with an angular resolution of about 0.01° at the cost of beam throughput