The noise covariance matrix computed between the signals from a microphone array is used in the design of spatial filters and beamformers with applications in noise suppression and dereverberation. This paper specifically addresses the problem of estimating the covariance matrix associated with a noise field when the array is rotating during desired source activity, as is common in head-mounted arrays. We propose a parametric model that leads to an analytical expression for the microphone signal covariance as a function of the array orientation and array manifold. An algorithm for estimating the model parameters during noise-only segments is proposed and the performance shown to be improved, rather than degraded, by array rotation. The stored model parameters can then be used to update the covariance matrix to account for the effects of any array rotation that occurs when the desired source is active. The proposed method is evaluated in terms of the Frobenius norm of the error in the estimated covariance matrix and of the noise reduction performance of a minimum variance distortionless response beamformer. In simulation experiments the proposed method achieves 18 dB lower error in the estimated noise covariance matrix than a conventional recursive averaging approach and results in noise reduction which is within 0.05 dB of an oracle beamformer using the ground truth noise covariance matrix.