A magnetic spectrometer is described for tagging a gamma-ray beam produced by Compton backscattering laser light from the electron beam circulating in a storage ring. The spectrometer, as it is now installed, has a design energy resolution of 5.5 MeV, a dispersion of 2.8 MeV/cm, and a dynamic range of 160 MeV. The energy resolution is limited by the energy spread of the stored beam. If dispersion can be introduced into the laser-electron interaction straight section of the storage ring, the resolution can be improved to be as small as 1.5 MeV, depending on the value of this dispersion. Measured properties of the spectrometer are in substantial agreement with the design values.