In this paper, we show that a multi-mode antenna (MMA) is an interesting alternative to a conventional phased antenna array for direction-of-arrival (DoA) estimation. By MMA we mean a single physical radiator with multiple ports, which excite different characteristic modes. In contrast to phased arrays, a closed-form mathematical model of the antenna response, like a steering vector, is not straightforward to define for MMAs. Instead one has to rely on calibration measurement or electromagnetic field (EMF) simulation data, which is discrete. To perform DoA estimation, array interpolation technique (AIT) and wavefield modeling (WM) are suggested as methods with inherent interpolation capabilities, fully taking antenna nonidealities like mutual coupling into account. We present a non-coherent DoA estimator for low-cost receivers and show how coherent DoA estimation and joint DoA and polarization estimation can be performed with MMAs. Utilizing these methods, we assess the DoA estimation performance of an MMA prototype in simulations for both 2D and 3D cases. The results show that WM outperforms AIT for high SNR. Coherent estimation is superior to non-coherent, especially in 3D, because non-coherent suffers from estimation ambiguities. In conclusion, DoA estimation with a single MMA is feasible and accurate.