We present ALMA observations of the 12CO (2–1) line of the newly born (tradio ~ 102 years) active galactic nucleus (AGN), PKS B1718–649. These observations reveal that the carbon monoxide in the innermost 15 kpc of the galaxy is distributed in a complex warped disk. In the outer parts of this disk, the CO gas follows the rotation of the dust lane and of the stellar body of the galaxy hosting the radio source. In the innermost kiloparsec, the gas abruptly changes orientation and forms a circumnuclear disk (r ≲ 700 pc) with its major axis perpendicular to that of the outer disk. Against the compact radio emission of PKS B1718–649 (r ~ 2 pc), we detect an absorption line at red-shifted velocities with respect to the systemic velocity (Δv = +365 ± 22 km s−1). This absorbing CO gas could trace molecular clouds falling onto the central super-massive black hole. A comparison with the near-infrared H2 1-0 S(1) observations shows that the clouds must be close to the black hole (r ≲ 75 pc). The physical conditions of these clouds are different from the gas at larger radii, and are in good agreement with the predictions for the conditions of the gas when cold chaotic accretion triggers an active galactic nucleus. These observations on the centre of PKS B1718–649 provide one of the best indications that a population of cold clouds is falling towards a radio AGN, likely fuelling its activity.