This paper presents a random rotation perturbation approach for privacy preserving data classification. Concretely, we identify the importance of classification-specific information with respect to the loss of information factor, and present a random rotation perturbation framework for privacy preserving data classification. Our approach has two unique characteristics. First, we identify that many classification models utilize the geometric properties of datasets, which can be preserved by geometric rotation. We prove that the three types of classifiers will deliver the same performance over the rotation perturbed dataset as over the original dataset. Second, we propose a multi-column privacy model to address the problems of evaluating privacy quality for multidimensional perturbation. With this metric, we develop a local optimal algorithm to find the good rotation perturbation in terms of privacy guarantee. We also analyze both naive estimation and ICA-based reconstruction attacks with the privacy model. Our initial experiments show that the random rotation approach can provide high privacy guarantee while maintaining zero-loss of accuracy for the discussed classifiers.