Radiation damage in a single crystal of ammonium sulfate caused by ${gamma}$-irradiation at room temperature has given rise to several paramagnetic centers. Electron spin resonance (ESR) spectra of crystal are obtained with the X-band EPR spectrometer at room temperature. An intense and isotropic peak of Gaussian shape at g = 2.0036 is assigned to $SO_3^-$, which shows power saturation effects. Angular dependence of spectra is studied for the rotations about three mutually perpendicular axes a, b and c. The g-values are obtained from the relative distances between isotropic peak of $SO_3^-$ and anisotropic peak of the species. Principal $g^-$values and direction cosines were calculated by diagonalizing the 3${ imes}$3 matrix whose elements are the $g^-$values for each species. From the analysis of characteristic principal $g^-$values and direction cosines for ammonium sulfate single crystal, anisotropic peaks corresponding to $SO_4^-,;SO_2^-$ and defect structure corresponding to electron excess type are identified.