Nonuniform rotational distortion (NURD) correction is vital for endoscopic optical coherence tomography (OCT) imaging and its functional extensions, such as angiography and elastography. Current NURD correction methods require time-consuming feature tracking/registration or cross-correlation calculations and thus sacrifice temporal resolution. Here we propose a cross-attention learning method for the NURD correction in OCT. Our method is inspired by the recent success of the self-attention mechanism in natural language processing and computer vision. By leveraging its ability to model long-range dependencies, we can directly obtain the spatial correlation between OCT A-lines at any distance, thus accelerating the NURD correction. We develop an end-to-end stacked cross-attention network and design three types of optimization constraints. We compare our method with two traditional feature-based methods and a CNN-based method on two publicly-available endoscopic OCT datasets. We further verify the NURD correction performance of our method on 3D stent reconstruction using a home-built endoscopic OCT system. Our method achieves a ?3?× speedup to real time (26?±?3 fps), and superior correction performance.