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Recent advances in large language models (LLMs) have enabled agentic AI systems that go beyond single-pass generation by combining reasoning with tool-mediated actions. Spatio-temporal domains are a natural but challenging setting for this paradigm, requiring agents to integrate heterogeneous modalities, operate under spatial and temporal constraints, and interact reliably with external resources such as GIS libraries, map services, and Earth observation pipelines. This survey provides a comprehensive overview of agentic AI for spatio-temporal intelligence and introduces a unified taxonomy spanning (i) spatio-temporal data modalities, (ii) core agentic capabilities, and (iii) the application landscape across geospatial analysis, remote sensing, urban planning, and mobility. A detailed paper list is provided at https://github.com/mohammadhashemii/awesome-agentic-AI-for-ST.