Weakly supervised person search aims to jointly detect and match persons with only bounding box annotations. Existing approaches typically focus on improving the features by exploring the relations of persons. However, scale variation problem is a more severe obstacle and under-studied that a person often owns images with different scales (resolutions). For one thing, small-scale images contain less information of a person, thus affecting the accuracy of the generated pseudo labels. For another, different similarities between cross-scale images of a person increase the difficulty of matching. In this paper, we address it by proposing a novel one-step framework, named Self-similarity driven Scale-invariant Learning (SSL). Scale invariance can be explored based on the self-similarity prior that it shows the same statistical properties of an image at different scales. To this end, we introduce a Multi-scale Exemplar Branch to guide the network in concentrating on the foreground and learning scaleinvariant features by hard exemplars mining. To enhance the discriminative power of the learned features, we further introduce a dynamic pseudo label prediction that progressively seeks true labels for training. Experimental results on two standard benchmarks, i.e., PRW and CUHKSYSU datasets, demonstrate that the proposed method can solve scale variation problem effectively and perform favorably against state-of-the-art methods