ABSTRACT Cell and organelle morphology are driven by diverse genetic and environmental factors and thus accurate quantification of cellular phenotypes is essential to experimental cell biology. Representation learning methods for phenotypic profiling map images to feature vectors that form an embedding space of morphological variation useful for clustering, dimensionality reduction, outlier detection, and supervised learning problems. Morphology properties do not change with orientation, and thus we argue that representation learning methods should encode this orientation invariance. We show that prior methods are sensitive to orientation, which can lead to suboptimal clustering. To address this issue, we develop O2-VAE, an unsupervised learning method that learns robust, orientation-invariant representations. We use O2-VAE to discover novel morphology subgroups in segmented cells and mitochondria, detect outlier cells, and rapidly characterise cellular shape and texture in large datasets, including in a newly generated synthetic benchmark.