RNA molecules can easily adopt alternative structures in response to different environmental conditions. As a result, a molecule's energy landscape is rough and can exhibit a multitude of deep basins. In the absence of a high-resolution structure, small-angle X-ray scattering data (SAXS) can narrow down the conformational space available to the molecule and be used in conjunction with physical modeling to obtain high-resolution putative structures to be further tested by experiments. Because of the low resolution of these data, it is natural to implement the integration of SAXS data into simulations using a coarse-grained representation of the molecule, allowing for much wider searches and faster evaluation of SAXS theoretical intensity curves than with atomistic models. We present here the theoretical framework and the implementation of a simulation approach based on our coarse-grained model HiRE-RNA combined with SAXS evaluations "on-the-fly" leading the simulation toward conformations agreeing with the scattering data, starting from partially folded structures as the ones that can easily be obtained from secondary structure prediction-based tools. We show on three benchmark systems how our approach can successfully achieve high-resolution structures with remarkable similarity with the native structure recovering not only the overall shape, as imposed by SAXS data, but also the details of initially missing base pairs.