Cross-domain named entity recognition (NER) is a crucial task in various practical applications, particularly when faced with the challenge of limited data availability in target domains. Existing methodologies primarily depend on feature representation or model parameter sharing mechanisms to enable the transfer of entity recognition capabilities across domains. However, these approaches often ignore the latent causal relationships inherent in invariant features. To address this limitation, we propose a novel framework, the Causal Structure Alignment-based Cross-Domain Named Entity Recognition (CSA-NER) framework, designed to harness the causally invariant features within causal structures to enhance the cross-domain transfer of entity recognition competence. Initially, CSA-NER constructs a causal feature graph utilizing causal discovery to ascertain causal relationships between entities and contextual features across source and target domains. Subsequently, it performs graph structure alignment to extract causal invariant knowledge across domains via the graph optimal transport (GOT) method. Finally, the acquired causal invariant knowledge is refined and utilized through the integration of Gated Attention Units (GAUs). Comprehensive experiments conducted on five English datasets and a specific CD-NER dataset exhibit a notable improvement in the average performance of the CSA-NER model in comparison to existing cross-domain methods. These findings underscore the significance of unearthing and employing latent causal invariant knowledge to effectively augment the entity recognition capabilities in target domains, thereby contributing a robust methodology to the broader realm of cross-domain natural language processing.