Many imaging modalities involve reconstruction of unknown objects from collections of noisy projections related by random rotations. In one of these modalities, cryogenic electron microscopy (cryo-EM), the extremely low signal-to-noise ratio (SNR) makes integration of information from multiple images crucial. Existing approaches to cryo-EM processing, however, either rely on handcrafted priors or apply deep learning only on select portions of the pipeline, such as particle picking, micrograph denoising, or refinement. A fully end-to-end reconstruction approach requires a neural network architecture that integrates information from multiple images while respecting the rotational symmetry of the measurement process. In this work, we introduce the polar transformer, a new neural network architecture that combines polar representations and transformers along with a convolutional attention mechanism that preserves the rotational symmetry of the problem. We apply it to the particle-level denoising problem, where it is able to learn discriminative features in the images, enabling optimal clustering, alignment, and denoising. On simulated datasets, this achieves up to a $2\times$ reduction in mean squared error (MSE) at a signal-to-noise ratio (SNR) of $0.02$, suggesting new opportunities for data-driven approaches to reconstruction in cryo-EM and related tomographic modalities.