The current research on Role-Playing Conversational Agents (RPCAs) with Large Language Models (LLMs) primarily focuses on imitating specific speaking styles and utilizing character backgrounds, neglecting the depiction of deeper personality traits.~In this study, we introduce personality-infused role-playing for LLM agents, which encourages agents to accurately portray their designated personality traits during dialogues. We then propose PsyPlay, a dialogue generation framework that facilitates the expression of rich personalities among multiple LLM agents. Specifically, PsyPlay enables agents to assume roles with distinct personality traits and engage in discussions centered around specific topics, consistently exhibiting their designated personality traits throughout the interactions. Validation on generated dialogue data demonstrates that PsyPlay can accurately portray the intended personality traits, achieving an overall success rate of 80.31% on GPT-3.5. Notably, we observe that LLMs aligned with positive values are more successful in portraying positive personality roles compared to negative ones. Moreover, we construct a dialogue corpus for personality-infused role-playing, called PsyPlay-Bench. The corpus, which consists of 4745 instances of correctly portrayed dialogues using PsyPlay, aims to further facilitate research in personalized role-playing and dialogue personality detection.