Abstract: In this work, the polarization effects of a strongly magnetized quark-gluon plasma are studied at finite temperature. It is found that a background magnetic field can have a strong effect on the photon and dilepton emission rates. It affects not only the total rate but also the angular dependence. In particular, the Landau-level quantization leads to a nontrivial momentum dependence of the photon/dilepton anisotropic flow coefficient on transverse momentum. In the case of photon emission, nonzero coefficients \upsilon _n (with even n) have opposite signs at small and large values of the transverse momentum. Additionally, the \upsilon _n signs alternate with increasing n, and their approximate values decrease as 1/n^2 in magnitude. The anisotropy of dilepton emission is well-pronounced only at large transverse momenta and small invariant masses. The corresponding \upsilon _n coefficients are of the same magnitude and show a similar sign-alternative pattern with increasing n as in the photon emission. It is proposed that the anisotropy of the photon and dilepton emission may serve as indirect measurements of the magnetic field.