Recent advances in addressing isolated nuclear spins have opened up a path toward using nuclear-spin-based quantum bits. Local magnetic fields are normally used to coherently manipulate the state of the nuclear spin; however, electrical manipulation would allow for fast switching and spatially confined spin control. Here, we propose and demonstrate coherent single nuclear spin manipulation using electric fields only. Because there is no direct coupling between the spin and the electric field, we make use of the hyperfine Stark effect as a magnetic field transducer at the atomic level. This quantum-mechanical process is present in all nuclear spin systems, such as phosphorus or bismuth atoms in silicon, and offers a general route toward the electrical control of nuclear-spin-based devices.