With the widespread adoption of open-source code language models (code LMs), intellectual property (IP) protection has become an increasingly critical concern. While current watermarking techniques have the potential to identify the code LM to protect its IP, they have limitations when facing the more practical and complex demand, i.e., offering the individual user-level tracing in the black-box setting. This work presents CLMTracing, a black-box code LM watermarking framework employing the rule-based watermarks and utility-preserving injection method for user-level model tracing. CLMTracing further incorporates a parameter selection algorithm sensitive to the robust watermark and adversarial training to enhance the robustness against watermark removal attacks. Comprehensive evaluations demonstrate CLMTracing is effective across multiple state-of-the-art (SOTA) code LMs, showing significant harmless improvements compared to existing SOTA baselines and strong robustness against various removal attacks.