Abstract. Bosonic ultra-light dark matter (ULDM) would form cored density distributions at the center of galaxies. These cores, seen in numerical simulations, admit analytic description as the lowest energy bound state solution ("soliton") of the Schroedinger-Poisson equations. Numerical simulations of ULDM galactic halos 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, measured for the host halo in 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) eV, which has been invoked as a possible solution to the small-scale puzzles of CDM, is in tension with the data.