The resonant circular photogalvanic effect is observed in wurtzite (0001)-oriented GaN low-dimensional structures excited by infrared radiation. The current is induced by angular-momentum transfer of photons to the photoexcited electrons at resonant intersubband optical transitions in a GaN/AlGaN heterojunction. The signal reverses upon the reversal of the radiation helicity or, at fixed helicity, when the propagation direction of the photons is reversed. Making use of the tunability of the free-electron laser FELIX, we demonstrate that the current direction changes by sweeping the photon energy through the intersubband resonance condition, in agreement with theoretical considerations.