  We measure the branching fraction of the decay $B^- \to D^0 \rho(770)^-$
using data collected with the Belle II detector. The data contain 387 million
$B\overline{B}$ pairs produced in $e^+e^-$ collisions at the $\Upsilon(4S)$
resonance. We reconstruct $8360\pm 180$ decays from an analysis of the
distributions of the $B^-$ energy and the $\rho(770)^-$ helicity angle. We
determine the branching fraction to be $(0.939 \pm 0.021\mathrm{(stat)} \pm
0.050\mathrm{(syst)})\%$, in agreement with previous results. Our measurement
improves the relative precision of the world average by more than a factor of
two.
