In this paper, a compact, cost-effective, and fast rotary speckle projector (RSP) is designed and manufactured for high-precision three-dimensional (3D) face data acquisition. Compared with the common speckle projectors, RSP uses a simple speckle pattern design method and has a good performance in high-speed projection and compact structure, which allows a flexible balance between measurement accuracy and time cost in a real acquisition task. Using a carefully designed rotation angle of the speckle mask, temporally and spatially non-correlative speckle patterns in the measurement volume can be generated. The rotation angle of the speckle mask is carefully checked and optimally selected via detailed theoretical analysis, simulation, and experiments to ensure 3D reconstruction accuracy across the reconstruction area. Subsequently, a binocular 3D face imaging system composed of the RSP and two cameras is constructed. With captured stereo speckle image pairs, we adopted our previously well-established spatial-temporal correlation method to determine the disparity. The accuracy of the 3D face imaging system was verified by using a real face mask, which is standardized by a certified, high-precision industrial 3D scanner. The real face data collection under various expressions has demonstrated that the proposed system also has a good performance for 3D face imaging in dynamic scenes.