We report the first search for the elastic scatterings between cosmic-ray boosted sub-MeV dark matter (DM) and electrons in the PandaX-4T liquid xenon experiment. Sub-MeV DM particles can be accelerated by scattering with electrons in the cosmic rays and produce detectable electron recoil signals in the detector. Using the commissioning data from PandaX-4T of 0.63 tonne·year exposure, we set new constraints on DM-electron scattering cross sections for DM masses ranging from 10 eV/c^{2} to 3 keV/c^{2}.