Spin-polarization of an ultrarelativistic electron beam head-on colliding with an ultraintense laser pulse is investigated in the quantum radiation-reaction regime. We develop a Monte-Carlo method to model electron radiative spin effects in arbitrary electromagnetic fields by employing spin-resolved radiation probabilities in the local constant field approximation. Due to spin-dependent radiation reaction, the applied elliptically polarized laser pulse polarizes the initially unpolarized electron beam and splits it along the propagation direction into two oppositely transversely polarized parts with a splitting angle of about tens of milliradians. Thus, a dense electron beam with above 70% polarization can be generated in tens of femtoseconds. The proposed method demonstrates a way for relativistic electron beam polarization with currently achievable laser facilities.Introduction. Spin-polarized electron beams have been extensively employed to investigate matter properties, atomic and molecular structures [1][2][3]. In high-energy physics, relativistic polarized electron beams can be used to probe the nuclear structure [4,5], generate polarized photons [6,7] and positrons [6,8], study parity violation in Møller scattering [9] and new physics beyond the Standard Model [10]. There are many methods to generate polarized electron beams at low energies [1]. However, for relativistic electron beams, there are mainly two methods [11]. In the first method mostly used in the Stanford Linear Accelerator, the polarized electrons are first extracted from a photocathode (illuminated by a circularly polarized light) [12,13] and then, accelerated by the linear accelerator (alternatively one may use polarized electrons from spin filters [14] or beam splitters [15], with subsequent laser wakefield acceleration [16]). The second method is a direct way of polarization of a relativistic electron beam in a storage ring via radiative polarization (Sokolov-Ternov effect) [17][18][19][20][21][22][23][24]. The polarization time of the latter due to the synchrotron radiation is rather slow (typically from minutes to hours), since the magnetic fields of a synchrotron are too weak (in the order of 1 Tesla). The electrons are polarized transversely due to Sokolov-Ternov effect. As mostly longitudinal polarization is interesting in high-energy physics, spin rotation systems are applied [25]. Moreover, for creating polarized positron beams (also applicable for electrons) Compton scattering or Bremsstrahlung of circularly polarized lasers and successive pair creation are commonly used [26][27][28][29][30]. The polarization of relativistic electrons can be detected by Compton scattering [31], Møller scattering [32], or other methods.