In-context learning (ICL) enables large language models (LLMs) to adapt to new tasks by conditioning on demonstrations of question-answer pairs. Recently, ICL has been extended to allow tabular data to be used as demonstration examples by serializing individual records into natural language formats. However, it is well-known that LLMs can leak information from data it has been prompted on, and since tabular data often contain sensitive information, understanding how to protect tabular data used in ICL is a critical area of research. This work serves as an initial investigation into how differential privacy (DP) can be utilized to protect tabular data used in ICL. Specifically, we investigate the application of DP mechanisms for private tabular ICL via data privatization prior to serialization and prompting. We formulate two private ICL frameworks with provable privacy guarantees in both the local (LDP-TabICL) and global (GDP-TabICL) DP scenarios via injecting noise into individual records or group statistics, respectively. Our evaluations show that DP-based ICL can protect the privacy of the underlying tabular data while achieving comparable performance to non-LLM baselines, especially under high privacy regimes.