The quantum spin Hall insulator is characterized by helical edge states, with the spin polarization of the electron being locked to its direction of motion. Although the edge-state conduction has been observed, unambiguous evidence of the helical spin texture is still lacking. Here, we investigate the coherent edge-state transport in an interference loop pinched by two point contacts. Because of the helical character, the forward interedge scattering enforces a π spin rotation. Two successive processes can only produce a nontrivial 2π or trivial 0 spin rotation, which can be controlled by the Rashba spin-orbit coupling. The nontrivial spin rotation results in a geometric π Berry phase, which can be detected by a π phase shift of the conductance oscillation relative to the trivial case. Our results provide smoking gun evidence for the helical spin texture of the edge states. Moreover, it also provides the opportunity to all electrically explore the trajectory-dependent spin Berry phase in condensed matter.