Trained on various human-authored corpora, Large Language Models (LLMs) have demonstrated a certain capacity to be prompted towards reflecting specific human-like traits (e.g., personality or values), benefiting downstream personalized LLMs and social simulations. However, current methods suffer from superficial elicitation: LLMs are only steered to mimic shallow, unstable stylistic patterns, failing to embody the desired traits precisely and consistently across diverse tasks like humans. To address this challenge, we propose IROTE, a novel in-context method for stable and transferable trait elicitation. Drawing on psychological theories that traits are formed through identity-related reflection, our method automatically generates and optimizes a textual self-reflection within prompts, which comprises self-perceived experience, to stimulate LLMs' trait-driven behavior. The optimization is performed by iteratively maximizing an information-theoretic objective that enhances the connections between LLMs' behavior and the target trait, while reducing noisy redundancy in reflection without any fine-tuning, leading to evocative and compact trait reflection. Extensive experiments across three human trait systems manifest that one single IROTE-generated self-reflection can induce LLMs' stable impersonation of the target trait across diverse downstream tasks beyond simple questionnaire answering, consistently outperforming existing strong baselines.