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Ferroelectric materials hold great potential for alternative memories and computing, but several challenges need to be overcome before bringing the ideas to applications. In this context, the recently discovered link between electric polarization and spin textures in some classes of ferroelectrics expands the perspectives of the design of devices that could simultaneously benefit from ferroelectric and spintronic properties. Here, we explore the concept of non-volatile ferroelectric control of charge-to-spin conversion in semimetallic WTe$_2$, which may provide a way for non-destructive read-out of the polar state. Based on the first-principles simulations, we show that the Rashba-Edelstein effect (REE) that converts electric currents into spin accumulation switches its sign upon the reversal of the electric polarization. The numerical values of REE, calculated for the first time for both bulk and bilayer WTe$_2$, demonstrate that the conversion is sizable, and may remain large even at room temperature. The ferroelectric control of spin transport in non-magnetic materials provides functionalities similar to multiferroics and allows the design of memories or logic-in-memory devices that combine ferroelectric writing of information at low power with the spin-orbit read-out of state.