Utilizing the state-independent projection technique, we obtain a general formula for the cyclotron-transition linewidth for anisotropic deformation potential phonon scattering. The formula is applied to calculate the width in Ge at low temperatures. It is shown that the transition between the two lowest adjacent Landau levels makes the most contribution to the temperature and the magnetic field dependence of the width, and the result agrees better with the experiment as the higher-order contributions are included. The width increases with the magnetic field, implying that the interaction of electrons with acoustic phonons increases with the field.