In situ generation of a high-energy, high-current, spin-polarized electron beam is an outstanding scientific challenge to the development of plasma-based accelerators for high-energy colliders. In this Letter, we show how such a spin-polarized relativistic beam can be produced by ionization injection of electrons of certain atoms with a circularly polarized laser field into a beam-driven plasma wakefield accelerator, providing a much desired one-step solution to this challenge. Using time-dependent Schrödinger equation (TDSE) simulations, we show the propensity rule of spin-dependent ionization of xenon atoms can be reversed in the strong-field multiphoton regime compared with the non-adiabatic tunneling regime, leading to high total spin polarization. Furthermore, three-dimensional particle-in-cell simulations are incorporated with TDSE simulations, providing start-to-end simulations of spin-dependent strong-field ionization of xenon atoms and subsequent trapping, acceleration, and preservation of electron spin polarization in lithium plasma. We show the generation of a high-current (0.8 kA), ultralow-normalized-emittance (∼37 nm), and high-energy (2.7 GeV) electron beam within just 11 cm distance, with up to ∼31% net spin polarization. Higher current, energy, and net spin-polarization beams are possible by optimizing this concept, thus solving a long-standing problem facing the development of plasma accelerators.