The Edelstein effect, which enables charge-to-spin conversion and is therefore highly promising for future spintronic devices, can be realized and non-volatilely manipulated in ferroelectric materials owing to their broken inversion symmetry and switchable polarization states. To date, most ferroelectric systems reported to exhibit the Edelstein effect are semiconductors, requiring extrinsic doping for functionality. In contrast, the Edelstein effect has rarely been reported in metallic ferroelectric systems, where doping is unnecessary. Using first-principles calculations, we predict that a pronounced Edelstein effect can be realized in the recently proposed intrinsic two-dimensional ferroelectric metal PtBi₂ monolayer, where the sign of the Edelstein coefficient is coupled to the direction of ferroelectric polarization through the polarization-switching-induced reversal of spin textures, thereby enabling non-volatile control of charge-spin conversion. The Edelstein effect reaches a magnitude of 10¹¹ ℏ / (A cm), which is sizable compared to previously reported ferroelectric systems. Microscopically, the Edelstein effect in a PtBi₂ monolayer originates from competing contributions of inner Rashba-like electron pockets and outer hole pockets with opposite signs; an upward shift of the Fermi level alters their balance and can reverse the sign of the Edelstein effect. Upon applying biaxial strain, the Fermi-surface electronic structure is strongly modified, resulting in a pronounced change of the Edelstein effect: a 2% compressive strain suppresses the Edelstein effect by about 50%. Our results not only identify a promising material platform for tunable charge-spin conversion but also provide new insights into the functional potential of metallic ferroelectric systems.