In this paper we present an investigation of the electron spin resonance (ESR) line shape of ammonium tartrate (AT) dosimeters exposed to radiation with different linear energy transfer (LET). We exposed our dosimeters to gamma-ray photons ((60)Co), 7 MeV and 14 MeV initial energy electrons, and 19.3 MeV initial energy protons. The differences in the power saturation behavior of ESR spectra of AT irradiated with photons, electrons and protons could be correlated to the effective LET of the radiation beams. We analyzed the behavior of peak-to-peak amplitude as a function of microwave power, and we developed a fitting procedure that permits us to obtain the dependence of the homogeneity parameter of the line shape on the LET of the radiation using the Castner saturation theory. This simple procedure allows us to distinguish the LET of the radiation beam.