Noisy Intermediate-Scale Quantum (NISQ) devices have begun to exhibit early quantum advantages on classically intractable problems, spanning physics simulations to Gaussian boson sampling. Yet, realizing these benefits remains challenging for non-experts, primarily due to the complexities of programming in Open Quantum Assembly Language (OpenQASM). Although Large Language Model (LLM)-based agents have shown promise in automating classical programming workflows, their quantum counterparts have largely been restricted to specialized tasks such as quantum chemistry or error correction. In this paper, we present QAgent, an LLM-powered multi-agent system that fully automates OpenQASM programming. By integrating task planning, in-context few-shot learning, retrieval-augmented generation (RAG) for long-term context, predefined generation tools, and chain-of-thought (CoT) reasoning, the agents systematically improve both compilation and functional correctness. Our evaluations demonstrate substantial improvements: across multiple LLMs of varying sizes, QAgent enhances the accuracy of QASM code generation by 71.6\% compared to previous static LLM-based approaches. We envision this multi-agent system as a key enabler for democratizing quantum programming, bridging expertise gaps, and accelerating the practical adoption of quantum computing.