Luminosity is a measure of the colliding frequency between beam and target and it is a crucial parameter for the measurement of absolute values, such as reaction cross sections. In this paper, we make use of experimental data from the ESR storage ring to demonstrate that the luminosity can be precisely determined by modelling the measured Rutherford scattering distribution. The obtained results are in good agreement with an independent measurement based on the x-ray normalization method. Our new method provides an alternative way to precisely measure the luminosity in low-energy stored-beam configurations. This can be of great value in particular in dedicated low-energy storage rings where established methods are difficult or impossible to apply.