The spin of a black hole is an important parameter which may be responsible for the properties of the inflow and outflow of the material surrounding the black hole. The broad-band infrared (IR)/optical/ultraviolet (UV) spectrum of the quasar SDSS J094533.99+100950.1 is clearly disc-dominated, with the spectrum peaking in the observed frequency range. Therefore, the disc-fitting method usually used for Galactic black holes can be used in this object to determine the black hole spin. We develop a numerical code for computing disc properties, including a radius-dependent hardening factor, and apply the ray-tracing method to incorporate all general relativity effects in light propagation. We show that the simple multicolour disc model gives a good fit, without requiring any other component, and the disc extends down to the marginally stable orbit. The best-fitting accretion rate is 0.13, well below the Eddington limit, and the black hole spin is moderate, 0.3. The contour error for the fit combined with the constraints for the black hole mass and the disc inclination gives a constraint that the spin is lower than 0.8. We discuss the sources of possible systematic errors in the parameter determinations.