This paper addresses the construction of a novel efficient rotation-invariant texture retrieval method that is based on the alignment in angle of signatures obtained via a steerable sub-Gaussian model. In our proposed scheme, we first construct a steerable multivariate sub-Gaussian model, where the fractional lower-order moments of a given image are associated with those of its rotated versions. The feature extraction step consists of estimating the so-called covariations between the orientation subbands of the corresponding steerable pyramid at the same or at adjacent decomposition levels and building an appropriate signature that can be rotated directly without the need of rotating the image and recalculating the signature. The similarity measurement between two images is performed using a matrix-based norm that includes a signature alignment in angle between the images being compared, achieving in this way the desired rotation-invariance property. Our experimental results show how this retrieval scheme achieves a lower average retrieval error, as compared to previously proposed methods having a similar computational complexity, while at the same time being competitive with the best currently known state-of-the-art retrieval system. In conclusion, our retrieval method provides the best compromise between complexity and average retrieval performance.