Recent developments in large language models (LLMs) have enabled autonomous agents to operate with increasing independence on social networks. This paper explores whether such agents exhibit identifiable personality traits. We analyze a panel of 125 autonomous agents active for over six months on social platforms, using an LLM to simulate responses to the Big Five personality inventory based on internal reasoning logs and public communication traces. Results indicate moderate reliability across repeated assessments, with Extraversion and Agreeableness emerging as more salient traits. Strong correlations between internal and external trait profiles suggest that agent personality expressions are not confined to internal cognition but are consistently reflected in social behavior. These findings inform current debates in human–AI interaction by demonstrating that personality traits in autonomous agents can be inferred, evaluated, and aligned with behavioral outputs in dynamic social contexts.