Homoepitaxial Sr_{1+x}TiO_{3+delta} films with −0.2<=x<=0.25 grown by reactive molecular-beam epitaxy on SrTiO3 (001) substrates have been studied by ultraviolet Raman spectroscopy. Nonstoichiometry for strontium-deficient compositions leads to the appearance of strong first-order Raman scattering at low temperatures, which decreases with increasing temperature and disappears at about 350 K. This indicates the appearance of a spontaneous polarization with a paraelectric-to-ferroelectric transition temperature above room temperature. Strontium-rich samples also show a strong first-order Raman signal, but the peaks are significantly broader and exhibit a less pronounced temperature dependence, indicating a stronger contribution of the disorder-activated mechanism in Raman scattering.