Optical helicity provides us with an effective means to control the helicity-dependent photocurrent in the spin-momentum-locked surface states of topological insulators (TIs). Also, the TIs show potential in polarization detection as an intrinsic solid-state optical chirality detector for easier integration and fabrication. However, the complex photoresponses with the circular photogalvanic effect, the linear photogalvanic effect, and the photon drag effect in the TIs prevent them from direct chirality detection of the elliptically polarized light. Here, by fitting with the theoretical models to the measured photocurrents, the microscopic origin of different components of the helicity-dependent photocurrent has been demonstrated. We show a comprehensive study of the helicity-dependent photocurrent in (Bi1-xSbx)2Te3 thin films of different thicknesses as a function of the light incident angle and the gate-tuned chemical potential. The observation of the light incident angle dependence of the helicity-dependent photocurrent provides us with a polarization detection strategy using a TI thin film without the use of any additional optical elements, and the detection accuracy can be enhanced by gate tuning. Additionally, the Stokes parameters can be extracted by arithmetic operation of photocurrents measured with different incident angles and gating voltages for complete characterization of the polarization states of a light beam. Using this means, we realize the polarization detection and the Stokes parameters analysis with a single device. Our work provides an alternative solution to develop miniaturized intrinsic polarization-sensitive photodetectors.