In order to investigate the impact of radio jets on the interstellar medium (ISM) of galaxies hosting active galactic nuclei (AGN), we present subarcsecond-resolution Atacama Large Millimeter/submillimeter Array (ALMA) CO(2-1) and CO(3-2) observations of the Teacup galaxy. This is a nearby (DL = 388 Mpc) radio-quiet type-2 quasar (QSO2) with a compact radio jet (Pjet ≈ 1043 erg s−1) that subtends a small angle from the molecular gas disc. Enhanced emission line widths perpendicular to the jet orientation have been reported for several nearby AGN for the ionised gas. For the molecular gas in the Teacup, not only do we find this enhancement in the velocity dispersion but also a higher brightness temperature ratio (T32/T21) perpendicular to the radio jet compared to the ratios found in the galaxy disc. Our results and the comparison with simulations suggest that the radio jet is compressing and accelerating the molecular gas, and driving a lateral outflow that shows enhanced velocity dispersion and higher gas excitation. These results provide further evidence that the coupling between the jet and the ISM is relevant to AGN feedback even in the case of radio-quiet galaxies.