Digital volume correlation is a new experimental technique that allows the measurement of the full-field strain tensor in three dimensions. We describe the addition of rotational degrees of freedom into the minimization problem for digital volume correlation in order to improve the overall performance of the strain measurement. A parameterization of rotations that is particularly suited to the minimization problem is presented, based on the angle-axis representation of finite rotations. The partial derivative of both a normalized cross-correlation coefficient and the sum-of-squares correlation coefficient are derived for use with gradient-based minimization algorithms. The addition of rotation is shown to greatly reduce the measurement error when even small amounts of rigid body rotation are present in an artificially rotated test volume. In an aluminum foam sample loaded in compression, including rotational degrees of freedom produced smoother contours of minimum principal strain. Renderings of the aluminum foam architecture in areas of low, medium and high rotation showed material deformation pattern in detail.