A kinetic theory of nonlinear coupling of ion‐Bernstein waves with the kinetic Alfve´n wave in a plasma is developed using a guiding center formalism. The nonlinearity arises through the motion of ions. The coupling coefficient is simplified at the limit where the Alfve´n wave’s wavelength is larger than an ion Larmor radius, whereas the ion‐Bernstein waves may have arbitrary wavelengths. At power levels employed on large devices in the slow wave ion‐cyclotron heating scheme, the excitation of magnetic fluctuations appears a genuine possibility.