We measure the branching fraction of the decay <math><msup><mi>B</mi><mo>−</mo></msup><mo>→</mo><msup><mi>D</mi><mn>0</mn></msup><mi>ρ</mi><mo>(</mo><mn>770</mn><msup><mo>)</mo><mo>−</mo></msup></math> using data collected with the Belle II detector. The data contain 387 million <math><mi>B</mi><mover><mi>B</mi><mo>¯</mo></mover></math> pairs produced in <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> collisions at the <math><mrow><mrow><mi>ϒ</mi><mrow><mo>(</mo><mn>4</mn><mi>S</mi><mo>)</mo></mrow></mrow></mrow></math> resonance. We reconstruct <math><mn>8360</mn><mo>±</mo><mn>180</mn></math> decays from an analysis of the distributions of the <math><msup><mi>B</mi><mo>−</mo></msup></math> energy and the <math><mi>ρ</mi><mo>(</mo><mn>770</mn><msup><mo>)</mo><mo>−</mo></msup></math> helicity angle. We determine the branching fraction to be <math><mo>(</mo><mn>0.939</mn><mo>±</mo><mn>0.021</mn><mrow><mo>(</mo><mi>stat</mi><mo>)</mo></mrow><mo>±</mo><mn>0.050</mn><mrow><mo>(</mo><mi>syst</mi><mo>)</mo></mrow><mo>)</mo><mo>%</mo></math>, in agreement with previous results. Our measurement improves the relative precision of the world average by more than a factor of two.

Measurement of the branching fraction of the decay <math><msup><mi>B</mi><mo>−</mo></msup><mo>→</mo><msup><mi>D</mi><mn>0</mn></msup><mi>ρ</mi><mo>(</mo><mn>770</mn><msup><mo>)</mo><mo>−</mo></msup></math> at Belle II