RNA molecules adopt three-dimensional structures that are critical to their function and of interest in drug discovery. Few RNA structures are known, however, and predicting them computationally has proven challenging. We introduce a machine learning approach that enables identification of accurate structural models without assumptions about their defining characteristics, despite being trained with only 18 known RNA structures. The resulting scoring function, the Atomic Rotationally Equivariant Scorer (ARES), substantially outperforms previous methods and consistently produces the best results in community-wide blind RNA structure prediction challenges. By learning effectively even from a small amount of data, our approach overcomes a major limitation of standard deep neural networks. Because it uses only atomic coordinates as inputs and incorporates no RNA-specific information, this approach is applicable to diverse problems in structural biology, chemistry, materials science, and beyond.