Deep neural networks have recently been thoroughly investigated as a powerful tool for MRI reconstruction. There is a lack of research however regarding their use for a specific setting of MRI, namely non-Cartesian acquisitions. In this work, we introduce a novel kind of deep neural networks to tackle this problem, namely density compensated unrolled neural networks. We assess their efficiency on the publicly available fastMRI dataset, and perform a small ablation study. We also open source our code, in particular a Non-Uniform Fast Fourier transform for TensorFlow.