The spin of Cygnus X-1 is measured by fitting reflection models to Suzaku data covering the energy band 0.9-400 keV. The inner radius of the accretion disc is found to lie within 2 gravitational radii (r g=GM/c 2), and a value of is obtained for the dimensionless black hole spin. This agrees with recent measurements using the continuum fitting method by Gou et al. and of the broad iron line by Duro et al. The disc inclination is measured at , which is consistent with the recent optical measurement of the binary system inclination by Orosz et al. of 27°± 0°.8. We pay special attention to the emissivity profile caused by irradiation of the inner disc by the hard power-law source. The X-ray observations and simulations show that the index q of that profile deviates from the commonly used, Newtonian, value of 3 within 3r g, steepening considerably within 2r g, as expected in the strong gravity regime.