We propose a classification method for distinguishing atrial fibrillation from sinus rhythm in pulse-wave measurements obtained with a blood pressure monitor. This method combines recurrence-based plots with convolutional neural networks. Moreover, we devised a novel plot, with which our classification achieved specificity of 97.5%, sensitivity of 98.4%, and accuracy of 98.6%. These criteria are higher than previously reported results for measurements obtained with blood pressure monitors and are almost equal to statistical measures for methods based on electrocardiographs and photoplethysmographs.