We propose a new algorithm for the accurate detection and localization of copy-move forgeries, based on rotation-invariant features computed densely on the image. Dense-field techniques proposed in the literature guarantee a superior performance with respect to their keypoint-based counterparts, at the price of a much higher processing time, mostly due to the feature matching phase. To overcome this limitation, we resort here to a fast approximate nearest-neighbor search algorithm, PatchMatch, especially suited for the computation of dense fields over images. We adapt the matching algorithm to deal efficiently with invariant features, so as to achieve higher robustness with respect to rotations and scale changes. Moreover, leveraging on the smoothness of the output field, we implement a simplified and reliable postprocessing procedure. The experimental analysis, conducted on databases available online, proves the proposed technique to be at least as accurate, generally more robust, and typically much faster than the state-of-the-art dense-field references.