The ferromagnetic ground states of the half-Heusler compounds AuMnX (X = In, Sn, Sb) have been calculated in the framework of the local spin-density approximation (LSDA) to density functional theory (DFT). AuMnSn is computed to be a half-metallic ferromagnet, whereas AuMnIn and AuMnSb are not half-metallic, due to their different band filling. The computed relativistic electronic structures served as inputs to calculate the magneto-optical Kerr rotations and ellipticities for all three materials. In the case of AuMnSn the largest, zero-temperature, polar Kerr rotation has been found to be -0.45° at about 1 eV photon energy. The computed MOKE spectra of AuMnSn are in qualitative agreement with recent experiments. The largest Kerr rotations of AuMnIn and AuMnSb have been calculated to be +0.64° at 4.3 eV and -0.85° at 0.9 eV, respectively.