Large Language Models (LLMs) have shown their capabilities in solving tasks across various domains. Recently, they have found applications in automating the design of digital circuits. However, there remains a dearth of research investigating the use of LLMs in automating the design of analog circuits. In this work, we propose LADAC: Large Language Model-driven Auto-Designer for Analog Circuits, to assist analog circuit design. LADAC designates an LLM as a decision-making agent, which formulates optimized design strategies based on user specifications and foundational principles of analog circuit design expertise. We applied LADAC to design two kinds of amplifiers with open-loop gain over 80dB, and a ring oscillator with 100MHz oscillation frequency successfully, showing that LADAC is capable of designing analog circuits. Furthermore, it demonstrates the LLMs' potential for designing a broader range of analog circuits.