Pre-trained contextual vision-and-language (V&L) models have achieved impressive performance on various benchmarks. However, existing models require a large amount of parallel image-caption data for pre-training. Such data are costly to collect and require cumbersome curation. Inspired by unsupervised machine translation, we investigate if a strong V&L representation model can be learned through unsupervised pre-training without image-caption corpora. In particular, we propose to conduct ``mask-and-predict pre-training on text-only and image-only corpora and introduce the object tags detected by an object recognition model as anchor points to bridge two modalities. We find that such a simple approach achieves performance close to a model pre-trained with aligned data, on four English V&L benchmarks. Our work challenges the widely held notion that aligned data is necessary for V&L pre-training, while significantly reducing the amount of supervision needed for V&L models.