Many current deep learning approaches make extensive use of backbone networks pre-trained on large datasets like ImageNet, which are then fine-tuned to perform a certain task. In remote sensing, the lack of comparable large annotated datasets and the wide diversity of sensing platforms impedes similar developments. In order to contribute towards the availability of pre-trained backbone networks in remote sensing, we devise a self-supervised approach for pre-training deep neural networks. By exploiting the correspondence between geo-tagged audio recordings and remote sensing imagery, this is done in a completely label-free manner, eliminating the need for laborious manual annotation. For this purpose, we introduce the SoundingEarth dataset, which consists of co-located aerial imagery and audio samples all around the world. Using this dataset, we then pre-train ResNet models to map samples from both modalities into a common embedding space, which encourages the models to understand key properties of a scene that influence both visual and auditory appearance. To validate the usefulness of the proposed approach, we evaluate the transfer learning performance of pre-trained weights obtained against weights obtained through other means. By fine-tuning the models on a number of commonly used remote sensing datasets, we show that our approach outperforms existing pre-training strategies for remote sensing imagery. The dataset, code and pre-trained model weights will be available at https://github.com/khdlr/SoundingEarth.