We measure the branching fraction of the decay B-→D0ρ(770)- using data collected with the Belle II detector. The data contain 387 million BB ̄ pairs produced in e+e- collisions at the Υ(4S) resonance. We reconstruct 8360±180 decays from an analysis of the distributions of the B- energy and the ρ(770)- helicity angle. We determine the branching fraction to be (0.939±0.021(stat)±0.050(syst))%, in agreement with previous results. Our measurement improves the relative precision of the world average by more than a factor of two.