We study rotating black holes in Einstein–Yang–Mills–Higgs theory. These black holes emerge from static black holes with monopole hair when a finite horizon angular velocity is imposed. At critical values of the horizon angular velocity and the horizon radius, they bifurcate with embedded Kerr–Newman black holes. The non-Abelian black holes possess an electric dipole moment, but no electric charge is induced by the rotation. We deduce that gravitating regular monopoles possess a gyroelectric ratio gel=2.