Combining angle-resolved photoemission spectroscopy and density functional theory calculations, we addressed the surface electronic structure of bent SrTiO₃ (STO) (001) wafers. Using a custom-made device, we observe that the low-dimensional states that emerge at the STO (001) surface are robust to an external tensile strain of about 0.1%. Our results show that this value of strain is too small to sensibly alter the surface conduction band of STO, but, surprisingly, it is enough to shift the energy of the in-gap states. In order to access higher strain values of around 2%, standard for STO-based heterostructures, we performed density functional theory calculations of STO slabs under different strain configurations. The simulations predict that such levels of both compressive and tensile strain significantly alter the orbital splitting of the surface conduction band. Our study indicates that the strain generated in STO can tailor the electronic properties of its bare surface and of STO-based interfaces.