Wave absorption near the electron cyclotron gyrofrequency by the current‐carrying energetic tail in tokamak plasmas is investigated. It is shown that by the proper choice of the angle of propagation, strong wave damping occurs for wave frequencies much less than the central electron cyclotron frequency and that the extraordinary mode can be launched from the low magnetic field side of the torus. It is also found that wave absorption is weakly dependent on the perpendicular temperature of the resonant particles.