Topological insulators represent a new quantum state of matter that are insulating in the bulk but metallic on the edge or surface. In the Dirac surface state, it is well-established that the electron spin is locked with the crystal momentum. Here we report a new phenomenon of the spin texture locking with the orbital texture in a topological insulator Bi₂Se₃. We observe light-polarization-dependent spin texture of both the upper and lower Dirac cones that constitutes strong evidence of the orbital-dependent spin texture in Bi₂Se₃. The different spin texture detected in variable polarization geometry is the manifestation of the spin-orbital texture in the initial state combined with the photoemission matrix element effects. Our observations provide a new orbital degree of freedom and a new way of light manipulation in controlling the spin structure of the topological insulators that are important for their future applications in spin-related technologies.