We use a two-photon dressing field to create an effective vector gauge potential for Bose-Einstein-condensed Rb-87 atoms in the F=1 hyperfine ground state. These Raman-dressed states are spin and momentum superpositions, and we adiabatically load the atoms into the lowest energy dressed state. The effective Hamiltonian of these neutral atoms is like that of charged particles in a uniform magnetic vector potential whose magnitude is set by the strength and detuning of the Raman coupling. The spin and momentum decomposition of the dressed states reveals the strength of the effective vector potential, and our measurements agree quantitatively with a simple single-particle model. While the uniform effective vector potential described here corresponds to zero magnetic field, our technique can be extended to nonuniform vector potentials, giving nonzero effective magnetic fields.