The magnetic anisotropy of epitaxial Fe films with thicknesses in the range of 2-142 monolayers (ML) grown on 4x2 reconstructed InAs(001) was investigated by in situ ferromagnetic resonance. The easy magnetization direction was found to be parallel to the [1[1]0]-direction for Fe films below 4 ML, while it rotates by 45^° toward the [100]-direction. It is observed that both surface-interface and volume contribution to the perpendicular anisotropy favor an easy axis perpendicular to the film plane. The cubic surface-interface anisotropy is relatively large with easy axes along 〈1[1]0〉-directions in contrast to the volume contribution which favors easy axes along the 〈110〉-directions. The volume contribution is found to be larger than the Fe bulk cubic anisotropy. A thickness independent uniaxial anisotropy has been found in films with a thickness of 2 up to 142 ML.