A popular approach to detect outliers in a data set is to find the largest consensus set, that is to say maximizing the number of inliers and estimating the underlying model. RANSAC is the most widely used method for this aim but is non-deterministic and does not guarantee to return the optimal solution. In this paper, we consider a rotation model and we present a new approach that performs consensus set maximization in a mathematically guaranteed globally optimal way. We solve the problem by a branch-and-bound framework associated with a rotation space search. Our mathematical formulation can be applied for various computer vision tasks such as panoramic image stitching, 3D registration with a rotating range sensor and line clustering and vanishing point estimation. Experimental results with synthetic and real data sets have successfully confirmed the validity of our approach.