Galactic bars can drive cold gas inflows towards the centres of galaxies. The gas transport happens primarily through the so-called bar dust lanes, which connect the galactic disc at kpc scales to the nuclear rings at hundreds of pc scales much like two gig antic galactic rivers. Once in the ring, the gas can fuel star formation activity, galactic outflows, and central supermassive black holes. Measuring the mass inflow rates is therefore important to understanding the mass/energy budget and evolution of galactic nuclei. In this work, we use CO datacubes from the PHANGS-ALMA survey and a simple geometrical method to measure the bar-driven mass inflow rate on to the nuclear ring of the barred galaxy NGC 1097. The method assumes that the gas velocity in the bar lanes is parallel to the lanes in the frame co-rotating with the bar, and allows one to derive the inflow rates from sufficiently sensitive and resolved position-position-velocity diagrams if the bar pattern speed and galaxy orientations are known. We find an inflow rate of M(over dot) = (3.0 +/- 2.1) M-circle dot yr (-1) averaged over a time span of 40 Myr, which varies by a factor of a few over time-scales of similar to 10 Myr. Most of the inflow appears to be consumed by star formation in the ring, which is currently occurring at a star formation rate (SFR) of similar or equal to 1.8-2 M-circle dot yr (-1), suggesting that the inflow is causally controlling the SFR in the ring as a function of time.