We extract large-angle elastic differential cross sections (DCSs) for electrons scattering from partially aligned O2+ and CO2+ molecules using rescattering photoelectrons generated by infrared laser pulses. The extracted DCSs are in good agreement with those calculated theoretically, demonstrating that accurate DCSs for electron-ion scattering can be extracted from the laser-induced rescattering spectra, thus paving the way for dynamic imaging of chemical reactions by rescattering photoelectron spectroscopy.