Robust data consistency using the Huber norm is proposed for compressed sensing radial MRI to reduce artifacts associated with outliers in the acquired data that cannot be removed by the sparse reconstruction. System imperfections such as chemical shift can introduce this type of large data distortions, or outliers. The quadratic shape of the usually employed Euclidean norm for data consistency is very sensitive to very large errors. In the proposed method, named RObust Golden-angle Radial Sparse Parallel MRI (ROGRASP), the Huber norm enables large errors to remain in the data discrepancy, not transferring them to the reconstructed image. In vivo acquisitions with outlier-contaminated data illustrate this improvement in quality for free-breathing cardiac MRI.