Helicity-dependent photocurrent (HDPC) and its modulation in topological insulator Bi2Te3 nanowires have been investigated. It is revealed that when the incident plane of a laser is perpendicular to the nanowire, the HDPC is an odd function of the incident angle, which is mainly contributed by the circular photogalvanic effect originating from the surface states of Bi2Te3 nanowire. When the incident plane of a laser is parallel to the nanowire, the HDPC is approximately an even function of the incident angle, which is due to the circular photon drag effect coming from the surface states. It is found that the HDPC can be effectively tuned by the back gate and the ionic liquid top gate. By analyzing the substrate dependence of the HDPC, we find that the HDPC of the Bi2Te3 nanowire on the Si substrate is an order of magnitude larger than that on SiO2, which may be due to the spin injection from the Si substrate to the Bi2Te3 nanowire. In addition, by applying different biases, the Stokes parameters of a polarized light can be extracted by arithmetic operation of the photocurrents measured in the Bi2Te3 nanowire. This work suggests that topological insulator Bi2Te3 nanowires may provide a good platform for opto-spintronic devices, especially in chirality and polarimtry detection.