Differential privacy (DP) is applied when fine-tuning pre-trained large language models (LLMs) to limit leakage of training examples. While most DP research has focused on improving a model's privacy-utility tradeoff, some find that DP can be unfair to or biased against underrepresented groups. In this work, we show the impact of DP on bias in LLMs through empirical analysis. Differentially private training can increase the model bias against protected groups w.r.t AUC-based bias metrics. DP makes it more difficult for the model to differentiate between the positive and negative examples from the protected groups and other groups in the rest of the population. Our results also show that the impact of DP on bias is not only affected by the privacy protection level but also the underlying distribution of the dataset.