We measure the spin of XTE J1550−564 using the two leading methods: (i) modelling the thermal continuum spectrum of the accretion disc; and (ii) modelling the broad red wing of the reflection fluorescence Fe Kα line. We find that these two independent measurements of spin are in agreement. For the continuum-fitting analysis, we use a data sample consisting of several dozen Rossi X-ray Timing Explorer spectra, and for the Fe Kα analysis, we use a pair of ASCA spectra from a single epoch. Our spin estimate for the black hole primary using the continuum-fitting method is −0.11 < a* < 0.71 (90 per cent confidence), with a most likely spin of a*= 0.34. In obtaining this result, we have thoroughly explored the dependence of the spin value on a wide range of model-dependent systematic errors and observational errors; our precision is limited by uncertainties in the distance and orbital inclination of the system. For the Fe-line method, our estimate of spin is a*= 0.55+0.15− 0.22. Combining these results, we conclude that the spin of this black hole is moderate, a*= 0.49+0.13− 0.20, which suggests that the jet activity of this microquasar is powered largely by its accretion disc rather than by the spin energy of the black hole.