A semi-analytical method is proposed to evaluate the dielectric response of a plasma to electromagnetic waves in the ion cyclotron domain of frequencies in a D-shaped but axisymmetric toroidal geometry. The actual drift orbit of the particles is accounted for. The method hinges on subdividing the orbit into elementary segments in which the integrations can be performed analytically or by tabulation, and it relies on the local book-keeping of the relation between the toroidal angular momentum and the poloidal flux function. Depending on which variables are chosen, the method allows computation of elementary building blocks for either the wave or the Fokker–Planck equation, but the accent is mainly on the latter. Two types of tangent resonance are distinguished.