Ferroelectricity is a potentially crucial issue in halide perovskites, breakthrough materials in photovoltaic research. Using density functional theory simulations and symmetry analysis, we show that the lead-free perovskite iodide (FA)SnI₃, containing the planar formamidinium cation FA, (NH₂CHNH₂)⁺, is ferroelectric. In fact, the perpendicular arrangement of FA planes, leading to a ‘weak’ polarization, is energetically more stable than parallel arrangements of FA planes, being either antiferroelectric or ‘strong’ ferroelectric. Moreover, we show that the ‘weak’ and ‘strong’ ferroelectric states with the polar axis along different crystallographic directions are energetically competing. Therefore, at least at low temperatures, an electric field could stabilize different states with the polarization rotated by π/4, resulting in a highly tunable ferroelectricity appealing for multistate logic. Intriguingly, the relatively strong spin–orbit coupling in noncentrosymmetric (FA)SnI₃ gives rise to a co-existence of Rashba and Dresselhaus effects and to a spin texture that can be induced, tuned and switched by an electric field controlling the ferroelectric state.