A new relativistic model for calculating (magnetic sublevel) electron-impact excitation process in plasmas is proposed in this paper, which is essential to predict the polarization property of x-ray radiation. Our model focuses on weakly coupled plasmas (assuming that the plasma is of low density and very hot), where we use a Debye-Hückel potential to represent the interactions among the charged particles, in order to calculate plasma shielding effects. As a practical example, we present results of accurate calculations of transition energy, cross section, and linear polarization of the photon emission following EIE of 1s2→1s2p3,1P1 lines of He-like Ar16+ ion over a broad range of energies and Debye lengths, i.e., 16 times ionized atom of Ar. Such highly-ionized species can exist in many environments, such as in laser-produced plasmas, x-ray laser, astrophysics, and inertial confinement fusion experiments. The energies and cross sections are found to be decreased with decreasing Debye length, these general characteristics also lead to a reduction in the linear polarization of the photon emission. The present approach compares well, with existing methods and experimental data. Apart from other applications, results obtained in this work should be useful in plasma diagnostic.