Because of the surface depolarization field, there is a critical thickness for ferroelectricity in ultrathin ferroelectric films, hindering miniaturization of high-density nonvolatile memory storage devices. A controllable Rashba effect by external electric field via switchable dipole moment could be a promising way to control and manipulate the spin degrees of freedom in spintronics. Here, based on first principles calculations, we show that non-planar Ag2Te monolayer, which has been recently predicted to be a topological insulator, possess a switchable out-of-plane electric dipole moment. The switching of the dipole can be realized by the penetration of Te atoms through the hexagonal Ag-plane. Additionally, non-planar Ag2Te shows a giant Rashba spin-splitting ( eV Å) due to the out-of-plane electric dipole moment. Our tight binding model indicates that the origin of such large is the large inversion symmetry breaking term ( eV), which is one order of magnitude larger in non-planar Ag2Te monolayer compared with other Rashba materials. Interestingly, the Rashba effect can be turned on/off by the phase transition from non-planar to planar structure via Te displacement. Moreover, the spin-texture can be completely reversed because of switchable electric dipole moment. Our work shows a new way to realize ferroelectric-like dipole moment switching and consequently switchable Rashba spin-splitting, which may facilitate a nonvolatile electrical control of the spin degrees of freedom, down to the monolayer thickness, promising potential applications to electrically controlled spintronic devices.