Estimating mental states such as cognitive workload from ElectroCardioGraphic (ECG) signals is a key but challenging step for many fields such as ergonomics, physiological computing, medical diagnostics or sport training. So far, the most commonly used machine learning algorithms to do so are linear classifiers such as Support Vector Machines (SVMs), often resulting in modest classification accuracies. However, Riemannian Geometry-based Classifiers (RGC), and more particularly the Tangent Space Classifiers (TSC), have recently shown to lead to state-of-the-art performances for ElectroEncephaloGraphic (EEG) signals classification. However, RGCs have never been explored for classifying ECG signals. Therefore, in this paper we design the first Riemannian geometry-based TSC for ECG signals, evaluate it for classifying two levels of cognitive workload, i.e., low versus high workload, and compare results to the ones obtained using an algorithm that is commonly used in the literature: the SVM. Our results indicated that the proposed ECG-TSC significantly outperformed an ECG-SVM classifier (a commonly used algorithm in the literature) when using 6, 10, 20, 30 and 40seconds time windows, suggesting an optimal time window length of 120 seconds (65.3% classification accuracy for the TSC, 57.8% for the SVM). Altogether, our results showed the value of RGCs to process ECG signals, opening the door to many other promising ECG classification applications.