Electron trapping by intense wave electric fields can alter the power deposition of electron‐cyclotron waves in a tokamak when high‐power sources are employed. The effect of wave trapping is examined in a ray‐tracing study that utilizes plasma and wave parameters appropriate for the Microwave Tokamak Experiment (MTX) [National Technical Information Service Document No. DE‐88016919 (1986)]. It is found that while wave trapping does result in some degradation in the rate of power deposition, single‐pass power deposition is expected to remain significant in MTX. In examining current drive for MTX, the influence of electron trapping in the magnetic wells of the tokamak equilibrium field is included. Relativistic and magnetic trapping effects reduce the driven current by 25% to 50%. This initial study does not include the effects of gradients in the magnetic field and wave vector and therefore provides lower bounds for the power deposition and driven current.