Free-space optical communications are highly sensitive to distortions induced by atmospheric turbulence. This is particularly relevant when using orbital angular momentum (OAM) to send information. As current machine learning techniques for computer vision allow for accurate classification of general images, we have studied the use of a convolutional neural network for recognition of intensity patterns of OAM states after propagation experiments in a laboratory. The effect of changes in magnification and level of turbulence were explored. An error as low as 2.39% was obtained for a low level of turbulence when the training and testing data came from the same optical setup. Finally, in this article we suggest data augmentation procedures to face the problem of training before the final calibration of a communication system, with no access to data for the actual magnification and level of turbulence of real application conditions.