Causal inference is the process of capturing cause-effect relationship among variables. Most existing works focus on dealing with structured data, while mining causal relationship among factors from unstructured data, like text, has been less examined, but is of great importance, especially in the legal domain. In this paper, we propose a novel Graph-based Causal Inference (GCI) framework, which builds causal graphs from fact descriptions without much human involvement and enables causal inference to facilitate legal practitioners to make proper decisions. We evaluate the framework on a challenging similar charge disambiguation task. Experimental results show that GCI can capture the nuance from fact descriptions among multiple confusing charges and provide explainable discrimination, especially in few-shot settings. We also observe that the causal knowledge contained in GCI can be effectively injected into powerful neural networks for better performance and interpretability.