The sliding motion of objects is typically governed by their friction with the underlying surface. Compared to translational friction, however, rotational friction has received much less attention. Here, we experimentally and theoretically study the rotational depinning and orientational dynamics of two-dimensional colloidal crystalline clusters on periodically corrugated surfaces in the presence of magnetically exerted torques. We demonstrate that the traversing of locally commensurate areas of the moiré pattern through the edges of clusters, which is hindered by potential barriers during cluster rotation, controls its rotational depinning. The experimentally measured depinning thresholds as a function of cluster size strikingly collapse onto a universal theoretical curve which predicts the possibility of a superlow-static-torque state for large clusters. We further reveal a cluster-size-independent rotation-translation depinning transition when lattice-matched clusters are driven jointly by a torque and a force. Our work provides guidelines to the design of nanomechanical devices that involve rotational motions on atomic surfaces.