We performed angle-resolved photoemission (ARPES) experiments on Bi2Te3 with circularly polarized light. ARPES data show very strong circular dichroism, indicating the existence of orbital angular momentum (OAM). Moreover, the alignment of OAM is found to have a strong binding energy dependence. Such energy dependence comes from a relatively strong band warping effect in Bi2Te3 compared to Bi2Se3. OAM close to the Dirac point has an ideal chiral structure (sinθ) without an out-of-plane component. The warping effect comes in as the binding energy decreases, and circular dichroism along a constant energy contour can no longer be explained by a simple sinθ function but requires a sin3θ term. When the warping effect becomes even stronger near the Fermi energy, circular dichroism gains an additional sin6θ term. Such behavior is found to be compatible with the theoretically predicted OAM structure.