We propose a disc–corona model in which a geometrically thin, optically thick disc surrounds a Kerr black hole, and magnetic fields exert a time-steady torque on the inner edge of the accretion disc. The analytical expression of the total gravitational power is derived from the thin-disc dynamics equations by using this new boundary condition. It is shown that the magnetic torque can considerably enhance the amount of energy released in the disc–corona system. Furthermore, the global solutions of this disc–corona system are obtained numerically. We find that the fraction of the power dissipated into the corona in the total for such a disc–corona system increases with increasing dimensionless black hole spin parameter a*, but is insensitive to Δɛ which is the additional radiative efficiency parameter relevant to magnetic torque, for Δɛ > 1. In addition, the emerged spectra from this disc–corona system are simulated by using the Monte Carlo method, and the effect of the different parameters on the output spectra is discussed.