Differential privacy is a cryptographically-motivated formal privacy definition that is robust against strong adversaries. The principal component analysis (PCA) algorithm is frequently used in signal processing, machine learning, and statistics pipelines. In many scenarios, private or sensitive data is distributed across different sites: in this paper we propose a differentially private distributed PCA scheme to enable collaborative dimensionality reduction. We investigate the performance of the proposed algorithm on synthetic and real datasets and show empirically that our algorithm can reach the same level of utility as the non-private PCA for some parameter choices, which indicates that it is possible to have meaningful utility while preserving privacy.