Advanced satellite-born remote sensing instruments produce high-resolution multi-spectral data for much of the globe at a daily cadence. These datasets open up the possibility of improved understanding of cloud dynamics and feedback, which remain the biggest source of uncertainty in global climate model projections. As a step towards answering these questions, we describe an automated rotation-invariant cloud clustering (RICC) method that leverages deep learning autoencoder technology to organize cloud imagery within large datasets in an unsupervised fashion, free from assumptions about predefined classes. We describe both the design and implementation of this method and its evaluation, which uses a sequence of testing protocols to determine whether the resulting clusters: (1) are physically reasonable, (i.e., embody scientifically relevant distinctions); (2) capture information on spatial distributions, such as textures; (3) are cohesive and separable in latent space; and (4) are rotationally invariant, (i.e., insensitive to the orientation of an image). Results obtained when these evaluation protocols are applied to RICC outputs suggest that the resultant novel cloud clusters capture meaningful aspects of cloud physics, are appropriately spatially coherent, and are invariant to orientations of input images. Our results support the possibility of using an unsupervised data-driven approach for automated clustering and pattern discovery in cloud imagery.