We show that the superconducting transition temperature Tc(H) of a very thin highly disordered film with strong spin-orbital scattering can be increased by parallel magnetic field H. This effect is due to polarization of magnetic impurity spins which reduces the full exchange scattering rate of electrons; the largest effect is predicted for spin-1 2 impurities. Moreover, for some range of magnetic impurity concentrations the phenomenon of superconductivity induced by magnetic field is predicted: superconducting transition temperature Tc(H) is found to be nonzero in the range of magnetic fields 0 < H * ≤ H ≤ Hc.The problem of superconducting alloys with magnetic impurities was addressed long ago by Abrikosov and Gor'kov (AG) [1]. They have shown that superconductivity (SC) is suppressed due to exchange scattering (ES) of electrons on magnetic impurities, the transition temperature T determined from the equation (hereafter, we employ units, in whichh = 1):Here ε = 2πT (m + 1/2) is the fermionic Matsubara frequency (m is integer), T c0 is the transition temperature of clean sample, and ν S = 2πN F n S J 2 S(S+1) is the ES rate of electrons on magnetic impurities (N F is the normal metal density of states per single spin state, n S is the concentration of magnetic impurities, J is the exchange coupling constant, and S is the impurity spin length). The solution of (1) yields the function T = T AG (ν S ). There exists a critical point at which the transition temperature is suppressed down to zero, the critical scattering rate being ν * S = π/(2e C ) T c0 = 0.882 T c0 , where C = 0.577 is the Euler constant. The critical concentration, corresponding to ν * S , is further denoted by n * S . We emphasize that ν S is the full ES rate, i.e. the sum of the spin flip scattering rate 2πN F n S J 2 ( S 2 x + S 2 y ) = 2/3 ν S and the rate of scattering without spin flip 2πN F n S J 2 S 2 z = 1/3 ν S . The AG's results were derived for unpolarized magnetic impurity spins. In this Letter we investigate how the polarization of impurity spins affects the ES mechanism of SC suppression. We show that polarization of magnetic impurity spins by external magnetic field reduces the full ES rate Γ(ε). It reaches its minimal value ν ∞ = ν S S/(S + 1) < ν S at the infinite field, when the impurity spins are completely polarized and spin flip processes have frozen out. This reduction is due to quantum fluctuations of impurity spins, thus it is strongest for S = 1/2 and vanishes in the limit S ≫ 1.If ES was the only mechanism of SC suppression in nonzero magnetic field h = µ B H, the transition temperature T • c (h). However, apart from ES, there are other mechanisms of SC suppression by magnetic field, namely, paramagnetic effect (PE) and orbital effect (OE). Thus, to observe an increase T c (h) > T c (0) of the actual transition temperature, PE and OE should be small compared to ES in the field range h ∼ T c (h). Strong reduction of PE is achieved in presence of high spin-orbital scattering rate ν so ≫ T c0 [2],[3], [4]. OE is suppressed f...