This paper describes a new technique for the alignment of crystal radiators used to produce high energy, linearly polarized photons via coherent bremsstrahlung scattering at electron beam facilities. In these experiments the crystal is mounted on a goniometer which is used to adjust its orientation relative to the electron beam. The angles and equations which relate the crystal lattice, goniometer and electron beam direction are presented here, and the method of alignment is illustrated with data taken at MAMI (the Mainz microtron). A practical guide to setting up a coherent bremsstrahlung facility and installing new crystals using this technique is also included.