Radiomics, quantitative feature extraction from radiological images, can improve disease diagnosis and prognostication. However, radiomic features are susceptible to image acquisition and segmentation variability. Ideally, only features robust to these variations would be incorporated into predictive models, for good generalisability. We extracted 93 radiomic features from carotid artery computed tomography angiograms of 41 patients with cerebrovascular events. We tested feature robustness to region-of-interest perturbations, image pre-processing settings and quantisation methods using both single- and multi-slice approaches. We assessed the ability of the most robust features to identify culprit and non-culprit arteries using several machine learning algorithms and report the average area under the curve (AUC) from five-fold cross validation. Multi-slice features were superior to single for producing robust radiomic features (67 vs. 61). The optimal image quantisation method used bin widths of 25 or 30. Incorporating our top 10 non-redundant robust radiomics features into ElasticNet achieved an AUC of 0.73 and accuracy of 69% (compared to carotid calcification alone AUC: 0.44, accuracy: 46%). Our results provide key information for introducing carotid CT radiomics into clinical practice. If validated prospectively, our robust carotid radiomic set could improve stroke prediction and target therapies to those at highest risk.