OBJECTIVE: To propose a 3D nonrigid registration method that accurately estimates the 3D displacement field from artifact-corrupted Coronary Magnetic Resonance Angiography (CMRA) images. METHODS: We developed a novel registration framework for registration of artifact-corrupted images based on a 3D U-Net initializer and a deep unrolling network. By leveraging a supervised learning framework with training labels estimated from fully-sampled images, the unrolling network learns a task-specific motion prior which reduces motion estimation biases caused by undersampling artifacts in the source images. We evaluated the proposed method, UNROLL, against an iterative Free-Form Deformation (FFD) registration method and a recently proposed Respiratory Motion Estimation network (RespME-net) for 6-fold (in-distribution) and 11-fold (out-of-distribution) accelerated CMRA. RESULTS: Compared to the baseline methods, UNROLL improved both the accuracy of motion estimation and the quality of motion-compensated CMRA reconstruction at 6-fold acceleration. Furthermore, even at 11-fold acceleration, which was not included during training, UNROLL still generated more accurate displacement fields than the baseline methods. The computational time of UNROLL for the whole 3D volume was only 2 seconds. CONCLUSION: By incorporating a learned respiratory motion prior, the proposed method achieves highly accurate motion estimation despite the large acceleration. SIGNIFICANCE: This work introduces a fast and accurate method to estimate the displacement field from low-quality source images. It has the potential to significantly improve the quality of motion-compensated reconstruction for highly accelerated 3D CMRA.