The harmonic relativistic ion cyclotron instability driven by MeV α-particles in thermal deuterium plasmas confined by non-uniform magnetic fields is studied with gyrokinetic theory. An integral dispersion equation is derived and solved numerically. The results provide clear evidence for the existence of the instability of α-particle cyclotron high harmonics in burning plasmas of one fast and one slow ion species. The characteristics of the modes are found to depend rather strongly on magnetic non-uniformity parameter and α-particle density.