In this paper we consider the problem of estimating the eigenvectors of the sample covariance matrix of decentralized measurements in a distributed fashion. The need for a distributed scheme is motivated by the many moment based methods that resort to the covariance of the data to extract information from the measurements. For large sensor network, gathering the data at a central processor generates a communication bottleneck. Our algorithm is based on a combination of the so called power method, that is used to compute the eigenvectors, and the average consensus protocol, that is utilized to structure the information exchange into a gossiping protocol. Our work shows how a completely distributed scheme based on near neighbors communications is feasible, and applies the proposed method to the estimation of the direction of arrival of a signal source.