Recently, Large Language Model (LLM)-empowered recommender systems (RecSys) have brought significant advances in personalized user experience and have attracted considerable attention. Despite the impressive progress, the research question regarding the safety vulnerability of LLM-empowered RecSys still remains largely under-investigated. Given the security and privacy concerns, it is more practical to focus on attacking the black-box RecSys, where attackers can only observe the system's inputs and outputs. However, traditional attack approaches employing reinforcement learning (RL) agents are not effective for attacking LLM-empowered RecSys due to the limited capabilities in processing complex textual inputs, planning, and reasoning. On the other hand, LLMs provide unprecedented opportunities to serve as attack agents to attack RecSys because of their impressive capability in simulating human-like decision-making processes. Therefore, in this paper, we propose a novel attack framework called CheatAgent by harnessing the human-like capabilities of LLMs, where an LLM-based agent is developed to attack LLM-Empowered RecSys. Specifically, our method first identifies the insertion position for maximum impact with minimal input modification. After that, the LLM agent is designed to generate adversarial perturbations to insert at target positions. To further improve the quality of generated perturbations, we utilize the prompt tuning technique to improve attacking strategies via feedback from the victim RecSys iteratively. Extensive experiments across three real-world datasets demonstrate the effectiveness of our proposed attacking method.