High-resolution x-ray spectra were recorded at the National Institute of Standards and Technology electron beam ion trap (EBIT) using two Johann-type crystal spectrometers, with their dispersion planes oriented parallel and perpendicular to the beam direction. The linear polarizations of the 1s2 − 1s2l transitions in He-like argon ions were determined from the measured spectra at electron beam energies of 3.87 and 7.91 keV. The theoretical analysis was performed using detailed collisional-radiative modeling of the non-Maxwellian EBIT plasma with the NOMAD code modified to account for magnetic sublevel atomic kinetics. Effects influencing the polarizations of the observed 1s2 − 1s2l lines were investigated, including radiative cascades, the 1s2 1S0 − 1s2s 1S0 two-photon transition, and the charge exchange recombination of H-like argon ions. With these included, the measured polarizations of the resonance (1s2 1S0 − 1s2p 1P1), intercombination (1s2 1S0 − 1s2p 3P1), and forbidden lines (1s2 1S0 − 1s2s 3S1, 1s2 1S0 − 1s2p 3P2 ) were found to be in good agreement with the calculations.