Large Language Models (LLMs) present substantial computational and memory challenges, particularly within their Feed-Forward Network (FFN) layers. While Computing-in-Memory (CIM) using Memristor offers a path to mitigate data movement bottlenecks, naively scaling existing CIM architectures for LLMs leads to new, severe communication overheads due to their typically isotropic (uniform) design. This paper introduces ASMA, an Anisotropy Scaling Memristor-based Accelerator, specifically co-designed for efficient LLM inference. ASMA identifies and exploits the inherent anisotropic scaling characteristics of LLM FFN layers—categorized into additive, concatenative, and sequential dimensions. Key innovations include a novel Subtile hierarchy for optimized pipelining, a hierarchical anisotropic Network-on-Chip (NoC) featuring distinct channels for broadcast and localized communication, and a co-designed compiler that maps LLM computations by leveraging these architectural specializations. Evaluations using a transaction-level simulator demonstrate that ASMA achieves latency improvement up to 81.7% and energy improvement up to 91.5% compared to conventional hierarchical CIM designs. ASMA offers a new paradigm for designing LLM-specific CIM accelerators by embracing workload anisotropy.