A theoretical model is developed for the effect of an electrostatic ion-cyclotron wave on central-cell ion confinement in a tandem mirror. Ion heating occurs in the central cell where the wave and local ion-cyclotron frequencies are equal. Coulomb pitch-angle collisions then scatter these ions into the loss region of velocity space. The wave heating is calculated analytically from the single-particle equations of motion, and the effect of collisions is modelled numerically by using a Monte-Carlo technique. A formula is obtained for the degradation of the ion-confinement time as a function of the RF wave amplitude. This formula reproduces the experimental results from the Livermore Tandem Mirror Experiment (TMX) as they are presented in a companion paper. The effect of the wave on density and temperature profiles is also calculated.