The magnetic-field-driven magnetization-reorientation phase transition in epitaxially grown Fe/GaAs(110) thin films (thickness 920 nm), first reported by Hathaway and Prinz, has been studied using anisotropic magnetoresistance (AMR) as a probe of the direction of magnetization. In AMR measurements, just as in ferromagnetic resonance (FMR), the ratios of the anisotropy constants to the magnetization are determined. In the present work the iron film thickness dependence of the ratios of the fourth-order (K1) and uniaxial (Ku) anisotropy constants to the magnetization were found comparable with previous FMR results. In addition, using values of the thickness dependence of the saturation magnetization, the present work includes the thickness dependence of K1 and Ku. The observed thickness dependence of K1 is similar to that seen previously in Ni/NaCl systems and may be due to strain-induced magnetostriction effects. Considerable hysteresis at the magnetization-reorientation transition is observed. The magnitude of the hysteresis is considerably less than that calculated from the anisotropy energies for uniform rotation of the magnetization. It is therefore reasonable to assume that the magnetization process occurs by domain-wall nucleation and propagation and that the hysteresis is associated with domain-wall pinning.