Rapid advances in Large Language Models (LLMs) create new opportunities by enabling efficient exploration of broad, complex design spaces. This is particularly valuable in computer architecture, where performance depends on microarchitectural designs and policies drawn from vast combinatorial spaces. We introduce Agentic Architect, an agentic AI framework for computer architecture design exploration and optimization that combines LLM-driven code evolution with cycle-accurate simulation. The human architect specifies the optimization target, seed design, scoring function, simulator interface, and benchmark split, while the LLM explores implementations within these constraints. Across cache replacement, data prefetching, and branch prediction, Agentic Architect matches or exceeds state-of-the-art designs. Our best evolved cache replacement design achieves a 1.062x geomean IPC speedup over LRU, 0.6% over Mockingjay (1.056x). Our evolved branch predictor achieves a 1.100x geomean IPC speedup over Bimodal, 1.5% over its Hashed Perceptron seed (1.085x). Finally, our evolved prefetcher achieves a 1.76x geomean IPC speedup over no prefetching, 17% over its VA/AMPM Lite seed (1.59x) and 21% over SMS (1.55x). Our analysis surfaces several findings about agentic AI-driven microarchitecture design. Across evolved designs, components often correspond to known techniques; the novelty lies in how they are coordinated. The architect's role is shifting, but the human remains central. Seed quality bounds what search can achieve: evolution can refine and extend an existing mechanism, but cannot compensate for a weak foundation. Likewise, objectives, constraints, and prompt guidance affect reliability and generalization. Overall, Agentic Architect is the first end-to-end open-source framework for agentic AI architecture exploration and optimization.