Spatio-Temporal Video Grounding (STVG) aims to retrieve the spatio-temporal tube of a target object or person in a video given a text query. Most existing approaches perform frame-wise spatial localization within a predicted temporal span, resulting in redundant computation, heavy supervision requirements, and limited generalization. Weakly-supervised variants mitigate annotation costs but remain constrained by the dataset-level train-and-fit paradigm with an inferior performance. To address these challenges, we propose the Agentic Spatio-Temporal Grounder (ASTG) framework for the task of STVG in an open-world and zero-shot setting. Specifically, two specialized agents SRA (Spatial Reasoning Agent) and TRA (Temporal Reasoning Agent) constructed leveraging modern Multi-modal Large Language Models (MLLMs) work collaboratively to retrieve the target tube in an autonomous and self-guided manner. Following a propose-and-evaluation paradigm, ASTG duly decouples spatio-temporal reasoning and automates the tube extraction, verification and temporal localization processes. With a dedicated visual memory and dialogue context, ASTG achieves architectural efficiency by minimizing the number of reasoning calls compared to exhaustive per-frame reasoning, eliminating the logical redundancy inherent in joint-reasoning systems. Experiments on popular benchmarks demonstrate the superiority of the proposed approach where it outperforms existing weakly-supervised and zero-shot approaches by a margin and is comparable to some of the fully-supervised methods.