The proficiency of Large Language Models (LLMs) in coding tasks is often a reflection of their extensive pre-training corpora, which typically collapses when confronted with previously unfamiliar programming languages. Departing from data-intensive finetuning, we investigate the paradigm of Inference-time Language Acquisition (ILA), where an LLM masters an unfamiliar language through dynamic interaction with limited external resources. In this paper, we propose ILA-agent, a general ILA framework that equips LLMs with a set of behavioral primitives. By modeling essential human-like behaviors as a suite of tools, ILA-agent enables LLMs to incrementally explore, apply, and verify language knowledge through structured interactions with the official documentation and execution environment. To provide a rigorous evaluation in a low-resource setting, we construct Cangjie-bench, a multi-task benchmark based on the novel statically-typed language Cangjie. We instantiate ILA-agent for Cangjie and evaluate its performance across code generation, translation, and program repair tasks. Results using diverse LLMs demonstrate that ILA-agent significantly outperforms retrieval-augmented baselines. Further analysis of agent trajectories characterizes the emergent behavior patterns while highlighting persisting performance gaps.