Bosonic ultra-light dark matter (ULDM) in the mass range m ~ $10^{-22} - 10^{-21} \rm eV$ has been invoked as a motivated candidate with new input for the small-scale `puzzles' of cold dark matter. Numerical simulations show that these models form cored density distributions at the center of galaxies ('solitons'). These works also found an empirical scaling relation between the mass of the large-scale host halo and the mass of the central soliton. We show that this relation predicts that the peak circular velocity of the outskirts of the galaxy should approximately repeat itself in the central region. Contrasting this prediction to the measured rotation curves of well-resolved near-by galaxies, we show that ULDM in the mass range m ~ $10^{-22} - 10^{-21} \rm eV$ is in tension with the data.