A complex-valued Hopfield neural network is a useful model for processing multi-level data. A rotor Hopfield network is an extension of a complex-valued Hopfield neural network but much more flexible. In addition, a rotor Hopfield neural network has excellent storage capacity and noise robustness characteristics. In the present work, we investigate the rotor Boltzmann machine (RoBM), a stochastic model of a rotor Hopfield neural network, through information geometry, which is a useful tool for analyzing stochastic models. We discuss RoBM through concepts of information geometry, such as the Fisher metric, parameters and potential functions. Moreover, we provide natural gradient descent learning and em-algorithms for RoBM as applications of information geometry.