Despite the importance of protein-RNA interactions in the cellular context, the number of available protein-RNA complex structures is still much lower than those of other biomolecules. As a consequence, few computational studies have been addressed towards protein-RNA complexes, and to our knowledge, no systematic benchmarking of protein-RNA docking has been reported. In this study we have extracted new pairwise residue-ribonucleotide interface propensities for protein-RNA, which can be used as statistical potentials for scoring of protein-RNA docking poses. We show here a new protein-RNA docking approach based on FTDock generation of rigid-body docking poses, which are later scored by these statistical residue-ribonucleotide potentials. The method has been successfully benchmarked in a set of 12 protein-RNA cases. The results show that FTDock is able to generate near-native solutions in more than half of the cases, and that it can rank near-native solutions significantly above random. In practically all these cases, our propensity-based scoring helps to improve the docking results, finding a near-native solution within rank 100 in 43% of them. In a remarkable case, the near-native solution was ranked 1 after the propensity-based scoring. Other previously described propensity potentials can also be used for scoring, with slightly worse performance. This new protein-RNA docking protocol permits a fast scoring of rigid-body docking poses in order to select a small number of docking orientations, which can be later evaluated with more sophisticated energy-based scoring functions.