The self-consistent technique for extracting density of states [DOS: g(E)] in an amorphous indium gallium zinc oxide (a-IGZO) thin film transistor is proposed and demonstrated. The key parameters are the g(E) of the a-IGZO active layer and the intrinsic channel mobility (mu(ch)). While the energy level (E) is scanned by the photon energy and gate-to-source voltage (V-GS) sweep, its density is extracted from an optical response of capacitance-voltage characteristics. Using the V-GS-dependent mu(ch) as another boundary condition, a linearly mapped DOS assuming a linear relation between V-GS and E is translated into a final DOS by fully considering a nonlinear relation between V-GS and E. The final DOS is finally extracted and verified by finding the self-consistent solution satisfying both the linearly mapped DOS and the measured V-GS dependence of mu(ch) with the numerical iteration of a DOS-based mu(ch) model. The extracted final DOS parameters are N-TA=1.73x10(17) cm(-3) eV(-1), N-DA=3.5x10(15) cm(-3) eV(-1), kT(TA)=0.023 eV, kT(DGA)=1.2 eV, and E-O=1.7 eV with the formula of exponential tail states and Gaussian deep states.