EEG signals have been reported to be informative and reliable for emotion recognition in recent years. However, the inter-subject variability of emotion-related EEG signals still poses a great challenge for the practical applications of EEG-based emotion recognition. Inspired by recent neuroscience studies on inter-subject correlation, we proposed a Contrastive Learning method for Inter-Subject Alignment (CLISA) to tackle the cross-subject emotion recognition problem. Contrastive learning was employed to minimize the inter-subject differences by maximizing the similarity in EEG signkal representations across subjects when they received the same emotional stimuli in contrast to different ones. Specifically, a convolutional neural network was applied to learn inter-subject aligned spatiotemporal representations from EEG time series in contrastive learning. The aligned representations were subsequently used to extract differential entropy features for emotion classification. CLISA achieved state-of-the-art cross-subject emotion recognition performance on our THU-EP dataset with 80 subjects and the publicly available SEED dataset with 15 subjects. It could generalize to unseen subjects or unseen emotional stimuli in testing. Furthermore, the spatiotemporal representations learned by CLISA could provide insights into the neural mechanisms of human emotion processing.