Electrochemical impedance spectroscopy (EIS) is widely used to probe electrochemical systems, with impedance spectra commonly interpreted through regression to equivalent circuit models (ECMs). However, ECM identification remains challenging due to structural non-uniqueness and the reliance on expert-driven model selection. Here, we present EIS-GPT, a transformer-based generative framework for ECM prediction that represents circuits as directed acyclic graphs and constructs candidate topologies autoregressively from impedance data. Reinforcement-learning-based fine-tuning is adapted to guide topology generation through reward functions that favor accurate spectral description while accounting for physical plausibility and model complexity. The framework produces candidate circuits that provide competitive spectral explanations while avoiding overfitting. By formulating ECM discovery as structure-aware generative optimization rather than categorical selection, EIS-GPT provides a scalable and transparent strategy for automated impedance model discovery across diverse electrochemical systems.