Recent advances in large language models have raised wide concern in generating abundant plausible source code without scrutiny, and thus tracing the provenance of code emerges as a critical issue. To solve the issue, we propose CodeMark, a watermarking system that hides bit strings into variables respecting the natural and operational semantics of the code. For naturalness, we novelly introduce a contextual watermarking scheme to generate watermarked variables more coherent in the context atop graph neural networks. Each variable is treated as a node on the graph and the node feature gathers neighborhood (context) information through learning. Watermarks embedded into the features are thus reflected not only by the variables but also by the local contexts. We further introduce a pre-trained model on source code as a teacher to guide more natural variable generation. Throughout the embedding, the operational semantics are preserved as only variable names are altered. Beyond guaranteeing code-specific properties, CodeMark is superior in watermarking accuracy, capacity, and efficiency due to a more diversified pattern generated. Experimental results show CodeMark outperforms the SOTA watermarking systems with a better balance of the watermarking requirements.