The local environment and oxidation state of the Fe impurity in strontium titanate are studied using XAFS spectroscopy. The influence of annealing temperature and deviation from stoichiometry on the possibility of incorporation of the impurity into the A and B sites of the perovskite structure is studied. The results obtained from the X-ray diffraction, XANES spectra, and EXAFS spectra suggest that at high annealing temperature the iron atoms, at least partially (up to 30%), enter the A sites in SrTiO3. The obtained results agree with results of first-principles calculations, according to which the iron at the A site exhibits strong off-centering (the displacement of ~1 Angstrom), similar to that previously established in SrTiO3 samples doped with Mn and Co.