A magnetic vortex is a curling magnetic structure realized in a ferromagnetic disk, which is a promising candidate for a memory cell for future non-volatile data-storage devices. Thus, an understanding of the stability and dynamical behaviour of the magnetic vortex is a major requirement for developing magnetic data-storage technology. Since the publication of experimental proof for the existence of a nanometre-scale core with out-of-plane magnetization in a magnetic vortex, the dynamics of vortices have been investigated intensively. However, a way to electrically control the core magnetization, which is a key for constructing a vortex-core memory, has been lacking. Here, we demonstrate the electrical switching of the core magnetization by using the current-driven resonant dynamics of the vortex; the core switching is triggered by a strong dynamic field that is produced locally by a rotational core motion at a high speed of several hundred metres per second. Efficient switching of the vortex core without magnetic-field application is achieved owing to resonance. This opens up the potentiality of a simple magnetic disk as a building block for spintronic devices such as a memory cell where the bit data is stored as the direction of the nanometre-scale core magnetization.