Recent experimental results have demonstrated ferroelectricity in thin films of SrTiO_{3} induced by antisite Ti_{Sr} defects. This opens a possibility to use SrTiO_{3} as a barrier layer in ferroelectric tunnel junctions (FTJs)-emerging electronic devices promising for applications in nanoelectronics. Here using density functional theory combined with quantum-transport calculations applied to a prototypical Pt/SrTiO_{3}/Pt FTJ, we demonstrate that the localized in-gap energy states produced by the antisite Ti_{Sr} defects are responsible for the enhanced electron tunneling conductance which can be controlled by ferroelectric polarization. Our tight-binding modeling, which takes into account multiple defects, shows that the predicted defect-assisted tunneling electroresistance effect is greatly amplified when the defect energy levels are brought to the Fermi energy by one of the polarization states. Our results have implications for FTJs based on conventional ferroelectric barriers with defects and can be employed for the design of new types of FTJs with enhanced performance.