We use ultrafast X-ray pulses to characterize the lattice response of SrTiO3 when driven by strong terahertz fields. We observe transient changes in the diffraction intensity with a delayed onset with respect to the driving field. Fourier analysis reveals two frequency components corresponding to the two lowest energy zone-center optical modes in SrTiO3. The lower frequency mode exhibits clear softening as the temperature is decreased while the higher frequency mode shows slight temperature dependence.