Configurations of rotating black holes in the cubic Galileon theory are computed by means of spectral methods. The equations are written in the 3+1 formalism and the coordinates are based on the maximal slicing condition and the spatial harmonic gauge. The black holes are described as apparent horizons in equilibrium. It enables the first fully consistent computation of rotating black holes in this theory. Several quantities are extracted from the solutions. In particular, the vanishing of the mass is confirmed. A link is made between that and the fact that the solutions do not obey the zeroth-law of black hole thermodynamics.