We calculate the leading order anomalous dimension of the transversity stru
cture function directly using three different methods, the local light-cone
expansion in the forward case, the non-forward case, and the short-distanc
e expansion of the forward Compton amplitude. Our results agree with the or
iginal calculation by Artru and Mekhfi [Z. Phys. 45 (1990) 669], which has
been doubted recently. We also comment on the next-to-leading order anomalo
us dimension.