We present a modeling study of x-ray line polarization in plasmas driven by high-intensity, ultrashort duration pulsed lasers. Electron kinetics simulations of these transient and nonequilibrium plasmas predict non-Maxwellian and anisotropic electron distribution functions. Under these conditions, the magnetic sublevels within fine structure levels can be unequally populated which leads to the emission of polarized lines. We have developed a time-dependent, collisional-radiative atomic kinetics model of magnetic sublevels to understand the underlying processes and mechanisms leading to the formation of polarized x-ray line emission in plasmas with anisotropic electron distribution functions. The electron distribution function consists of a thermal component extracted from hydrodynamic calculations and a beam component determined by PIC simulations of the laser-plasma interaction. We focus on the polarization properties of the He-like Si satellites of the L y_alpha line, discuss the time evolution of polarized satellite spectra, and identify suitable polarization markers that are sensitive to the anisotropy of the electron distribution function and can be used for diagnostic applications.