Two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs) are introducing new directions in the 2D materials landscape. The coexistence of ferroelectricity and spin-orbit interactions play a key role in their optoelectronic properties. We perform a detailed study on a recently synthesized ferroelectric 2D-HOIP, (AMP)PbI\(_4\) (AMP = 4-aminomethyl-piperidinium). The calculated polarization and Rashba parameter are in excellent agreement with experimental values. We report a striking new effect, i.e., an extraordinarily large Rashba anisotropy that is tunable by ferroelectric polarization: as polarization is reversed, not only the spin texture chirality is inverted, but also the major and minor axes of the Rashba anisotropy ellipse in k-space are interchanged - a pseudo rotation. A \(k \cdot p\) model Hamiltonian and symmetry-mode analysis reveal a quadrilinear coupling between the cation-rotation modes responsible for the Rashba ellipse pseudo-rotation, the framework rotation, and the polarization. These findings may provide new avenues for spin-optoelectronic devices such as spin valves or spin FETs.