The nonlinear lattice dynamics of La0.7Sr0.3MnO3, as initiated by strong mid-infrared femtosecond pulses made resonant with a specific lattice vibration, are measured with ultrafast X-ray diffraction at the LCLS free electron laser. Our experiments show that large amplitude excitation of an infrared-active stretching mode leads also to a displacive motion along the coordinate of a second, anharmonically coupled, Raman mode. This rectification of the vibrational field is described within the framework of the Ionic Raman Scattering theory and explains how direct lattice excitation in the nonlinear regime can induce a structural phase transition. •We disclose a microscopic mechanism of vibrationally induced phase transitions in correlated electron systems.•The resonantly excited IR-active phonon is rectified through lattice anharmonicities in the Ionic Raman Scattering model.•This effect results in a displacive excitation of the crystal lattice along a Raman phonon coordinate.•Femtosecond hard X-ray diffraction at a free electron laser was used for this study.