RNA-protein specific binding underlies a large variety of fundamental cellular processes. An atomistic description of such binding processes would aid the rational conception of pharmaceutical modulators of those functions. However, while the field of protein-protein docking has achieved considerable improvements in the last decade, protein-RNA docking encounters specific difficulties. This is mainly due to the flexibility and the large conformational space of RNAs compared to proteins, and especially single-stranded RNAs (ssRNAs). Here, we present a novel and highly effective fragment-based approach to tackle this problem, capable of accurate prediction of the structure of a ssRNA bound to a protein, starting from the structure of the protein and the sequence of the RNA. As a proof-of-principle, we focus on the common case of a uniform ssRNA sequence. Without any information on specific contacts or the RNA structure, our method permitted to define accurately the binding site on the protein with 10 Å precision, through the use of a comprehensive fragment library. Moreover, the bound conformation of the ssRNA could be sampled with ~1.5 Å RMSD on heavy atoms, a precision never reached so far. In future research, the method will be extended to dock arbitrary ssRNA sequences to protein structures.