Four-dimensional cone-beam computed tomography (4D CBCT) provides respiration-resolved images and can be used for image-guided radiation therapy. However, the ability to reveal respiratory motion comes at the cost of image artifacts. As raw projection data are sorted into multiple respiratory phases, there is a limited number of cone-beam projections available for image reconstruction. Consequently, the 4D CBCT images are covered by severe streak artifacts. Although several deep learning-based methods have been proposed to address this issue, most algorithms employ ordinary network models, neglecting the intrinsic structural prior within 4D CBCT images. In this paper, we first explore the origin and appearance of streak artifacts in 4D CBCT images.Specifically, we find that streak artifacts exhibit a periodic rotational motion along with the patient's respiration. This unique motion pattern inspires us to distinguish the artifacts from the desired anatomical structures in the spatiotemporal domain. Thereafter, we propose a spatiotemporal neural network named RSTAR-Net with separable and circular convolutions for Rotational Streak Artifact Reduction. The specially designed model effectively encodes dynamic image features, facilitating the recovery of 4D CBCT images. Moreover, RSTAR-Net is also lightweight and computationally efficient. Extensive experiments substantiate the effectiveness of our proposed method, and RSTAR-Net shows superior performance to comparison methods.