Large data collections required for the training of neural networks often contain sensitive information such as the medical histories of patients, and the privacy of the training data must be preserved. In this paper, we introduce a dropout technique that provides an elegant Bayesian interpretation to dropout, and show that the intrinsic noise added, with the primary goal of regularization, can be exploited to obtain a degree of differential privacy. The iterative nature of training neural networks presents a challenge for privacy-preserving estimation since multiple iterations increase the amount of noise added. We overcome this by using a relaxed notion of differential privacy, called concentrated differential privacy, which provides tighter estimates on the overall privacy loss. We demonstrate the accuracy of our privacy-preserving dropout algorithm on benchmark datasets.