We report on the observation of the giant photocurrents in HgTe/HgCdTe quantum well (QW) of critical thickness at which a Dirac spectrum emerges. At an exciting QW of 6.6 nm width by terahertz (THz) radiation and sweeping magnetic field we detected a resonant photocurrent. Remarkably, the position of the resonance can be tuned from negative (-0.4 T) to positive (up to 1.2 T) magnetic fields by means of optical doping. The photocurrent data, accompanied by measurements of radiation transmission as well as Shubnikov-de Haas and quantum Hall effects, prove that the photocurrent is caused by cyclotron resonance in a Dirac fermion system, which allows us to obtain the effective electron velocity v approximate to 7.2 x 10(5) m/s. We develop a microscopic theory of the effect and show that the inherent spin-dependent asymmetry of light-matter coupling in the system of Dirac fermions causes the electric current to flow.