The dependence on the torsion H = dh of the Wess-Zumino couplings of D-branes that are trivially embedded in space-time is studied. We show that even in this simple set-up some torsion components can be turned on, with a non-trivial effect on the RR couplings. in the special cases in which either the tangent or the normal bundle are trivial, the torsion dependence amounts to substitute the standard curvature with its generalization in the presence of torsion, in the usual couplings involving the roof genus (A) over cap. (C) 2001 Elsevier Science B.V. All rights reserved.