We give robust recovery results for synchronization on the rotation group, Formula omitted. In particular, we consider an adversarial corruption setting, where a limited percentage of the observations are arbitrarily corrupted. We develop a novel algorithm that exploits Tukey depth in the tangent space of Formula omitted. This algorithm, called Depth Descent Synchronization, exactly recovers the underlying rotations up to an outlier percentage of Formula omitted, which corresponds to 1/4 for Formula omitted and 1/8 for Formula omitted. In the case of Formula omitted, we demonstrate that a variant of this algorithm converges linearly to the ground truth rotations. We implement this algorithm for the case of Formula omitted and demonstrate that it performs competitively on baseline synthetic data.