With the rapid progress of LLMs, high quality generative text has become widely available as a cover for text steganography. However, prevailing methods rely on hand-crafted or pre-specified strategies and struggle to balance efficiency, imperceptibility, and security, particularly at high embedding rates. Accordingly, we propose Auto-Stega, an agent-driven self-evolving framework that is the first to realize self-evolving steganographic strategies by automatically discovering, composing, and adapting strategies at inference time; the framework operates as a closed loop of generating, evaluating, summarizing, and updating that continually curates a structured strategy library and adapts across corpora, styles, and task constraints. A decoding LLM recovers the information under the shared strategy. To handle high embedding rates, we introduce PC-DNTE, a plug-and-play algorithm that maintains alignment with the base model's conditional distribution at high embedding rates, preserving imperceptibility while enhancing security. Experimental results demonstrate that at higher embedding rates Auto-Stega achieves superior performance with gains of 42.2\% in perplexity and 1.6\% in anti-steganalysis performance over SOTA methods.