The magnetization of body-centered-cubic iron was measured by means of polarized neutron reflection on a set of films of different thickness (4, 6, 8, and 16 angstrom). The films were epitaxially deposited onto polished (100) MgO substrates and covered by protective layers of gold. The results show that at 40 K all films are ferromagnetic, with an average magnetic moment per iron equal to 2.2+/-0.2mu(B) regardless of film thickness. However, the thinnest films exhibit a Curie temperature lower than that of the bulk and a magnetization axis tilted out of the film surface. These results are discussed in the light of the detailed morphology of the films, and compared with the theoretical predictions.