Watermarking has emerged as an effective solution for copyright protection of synthetic data. However, applying watermarking techniques to synthetic tabular data presents challenges, as tabular data can easily lose their watermarks through shuffling or deletion operations. The major challenge is to provide traceability for tracking multiple users of the watermarked tabular data while maintaining high data utility and robustness (resistance to attacks). To address this, we design a multi-bit watermarking scheme TableMark that encodes watermarks into synthetic tabular data, ensuring superior traceability and robustness while maintaining high utility. We formulate the watermark encoding process as a constrained optimization problem, allowing the data owner to effectively trade off robustness and utility. Additionally, we propose effective optimization mechanisms to solve this problem to enhance the data utility. Experimental results on four widely used real-world datasets show that TableMark effectively traces a large number of users, is resilient to attacks, and preserves high utility. Moreover, TableMark significantly outperforms state-of-the-art tabular watermarking schemes.