  The anomalous dimensions of the general flavour non-singlet quark bilinear
currents \psi \gamma^{[\mu_1} ... \gamma^{\mu_n]} \psi are computed at three
loops in quantum chromodynamics in the minimal subtraction scheme. The
dimension of the tensor current emerges for the case n = 2 and the anomalous
dimension for the general flavour singlet current is also discussed.
