We consider the single-particle relaxation rate of 2D electrons subject to a random magnetic field. The density-of-states (DOS) oscillations in a uniform magnetic field (in addition to a random one) are studied. We define a gauge-invariant single-particle relaxation time as a parameter describing the amplitude of DOS oscillations. Unlike the conventional case of random potential scattering, the broadening of the Landau levels does not depend on magnetic field.