It is proposed to apply the radiative electron capture into high-Z projectiles as a probe process for measuring the spin polarization of the hydrogenlike ions at storage rings. We argue that such polarization measurements are possible since the linear polarization of emitted x-ray photons is greatly sensitive to the spin states of incoming ions with nuclear spin I > 1/2. In particular, for K-shell electron capture into the hydrogenlike ions, the linear polarization of light as measured out of the reaction plane is found to be proportional to the degree of ion polarization. Detailed computations for the dependence of the photon polarization on the ion spin states and projectile energies are carried out for the electron recombination into hydrogenlike Bi 82+ ions.