Topological insulators exhibit metallic surface states populated by massless Dirac fermions with spin-momentum locking, where the carrier spin lies in-plane, locked at right angles to the carrier momentum. Here, we show that a charge current produces a net spin polarization via spin-momentum locking in Bi2Se3 films, and this polarization is directly manifested as a voltage on a ferromagnetic contact. This voltage is proportional to the projection of the spin polarization onto the contact magnetization, is determined by the direction and magnitude of the charge current, scales inversely with Bi2Se3 film thickness, and its sign is that expected from spin-momentum locking rather than Rashba effects. Similar data are obtained for two different ferromagnetic contacts, demonstrating that these behaviours are independent of the details of the ferromagnetic contact. These results demonstrate direct electrical access to the topological insulators' surface-state spin system and enable utilization of its remarkable properties for future technological applications.