Powerful radio galaxies show evidence of ongoing active galactic nuclei (AGN) feedback, mainly in the form of fast, massive outflows. But it is not clear how these outflows affect the star formation of their hosts. We investigate the different manifestations of AGN feedback in the evolved, powerful radio source 3C 293 and their impact on the molecular gas of its host galaxy, which harbors young star-forming regions and fast outflows of H i and ionized gas. We study the distribution and kinematics of the molecular gas of 3C 293 using high spatial resolution observations of the ^12^CO(1-0) and ^12^CO(2-1) lines, and the 3mm and 1 continuum taken with the IRAM Plateau de Bure interferometer. We mapped the molecular gas of 3C 293 and compared it with the dust and star-formation images of the host. We searched for signatures of outflow motions in the CO kinematics, and re-examined the evidence of outflowing gas in the HI spectra. We also derived the star formation rate (SFR) and star formation efficiency (SFE) of the host with all available SFR tracers from the literature, and compared them with the SFE of young and evolved radio galaxies and normal star-forming galaxies. The ^12^CO(1-0) emission line shows that the molecular gas in 3C 293 is distributed along a massive (M(H_2_)~2.2x10^10^M_{sun}_) ~24" (21kpc) diameter warped disk, that rotates around the AGN. Our data show that the dust and the star formation are clearly associated with the CO disk. The ^12^CO(2-1) emission is located in the inner 7kpc (diameter) region around the AGN, coincident with the inner part of the ^12^CO(1-0) disk. Both the ^12^CO(1-0) and ^12^CO(2-1) spectra reveal the presence of an absorber against the central regions of 3C 293 that is associated with the disk. We do not detect any fast (500km/s) outflow motions in the cold molecular gas. The host of 3C 293 shows an SFE consistent with the Kennicutt-Schmidt law of normal galaxies and young radio galaxies, and it is 10-50 times higher than the SFE estimated with the 7.7um PAH emission of evolved radio galaxies. Our results suggest that the apparently low SFE of evolved radio galaxies may be caused by an underestimation of the SFR and/or an overestimation of the molecular gas densities in these sources. The molecular gas of 3C 293, while not incompatible with a mild AGN-triggered flow, does not reach the high velocities (500km/s) observed in the HI spectrum. We find no signatures of AGN feedback in the molecular gas of 3C 293.