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Text-based person search (TBPS) is of significant importance in intelligent surveillance, which aims to retrieve pedestrian images with high semantic relevance to a given text description. This retrieval task is characterized with both modal heterogeneity and fine-grained matching. To implement this task, one needs to extract multi-scale features from both image and text domains, and then perform the cross-modal alignment. However, most existing approaches only consider the alignment confined at their individual scales, e.g., an image-sentence or a region-phrase scale. Such a strategy adopts the presumable alignment in feature extraction, while overlooking the cross-scale alignment, e.g., image-phrase. In this paper, we present a transformer-based model to extract multi-scale representations, and perform Asymmetric Cross-Scale Alignment (ACSA) to precisely align the two modalities. Specifically, ACSA consists of a global-level alignment module and an asymmetric cross-attention module, where the former aligns an image and texts on a global scale, and the latter applies the cross-attention mechanism to dynamically align the cross-modal entities in region/image-phrase scales. Extensive experiments on two benchmark datasets CUHK-PEDES and RSTPReid demonstrate the effectiveness of our approach. Codes are available at \href{url}{https://github.com/mul-hjh/ACSA}.