With the rise of social media, misinformation has become increasingly prevalent, fueled largely by the spread of rumors. This study explores the use of Large Language Model (LLM) agents within a novel framework to simulate and analyze the dynamics of rumor propagation across social networks. To this end, we design a variety of LLM-based agent types and construct four distinct network structures to conduct these simulations. Our framework assesses the effectiveness of different network constructions and agent behaviors in influencing the spread of rumors. Our results demonstrate that the framework can simulate rumor spreading across more than one hundred agents in various networks with thousands of edges. The evaluations indicate that network structure, personas, and spreading schemes can significantly influence rumor dissemination, ranging from no spread to affecting 83\% of agents in iterations, thereby offering a realistic simulation of rumor spread in social networks.