Sentiment analysis is a crucial tool to evaluate customer opinion on products and services. However, analyzing social media data raises concerns about privacy violations since users may share sensitive information in their posts. In this work, we propose a privacy-preserving approach for sentiment analysis on Twitter data using Differential Privacy (DP). We first implement a non-private baseline model and assess the impact of various settings and preprocessing methods. We then extend this approach with DP under multiple privacy parameters ε = {0.1, 1, 10} and finally evaluate the usability of the resulting private models. Our results show that DP models can maintain high accuracy for the studied task. We contribute to the development of privacy-preserving machine learning for customer opinion analysis and provide insights into trade-offs between privacy and utility. The proposed approach helps protect sensitive information while still allowing for valuable insights to be gained from social media data.