A measurement of MeV-GeV linear polarization would provide information about the emission mechanisms of gamma-ray sources, especially pulsars and AGN (Active Galaxy Nuclei).
The $\textit{Fermi}$ Large Area Telescope ($\textit{Fermi}$-LAT) detects gamma rays between $20\,MeV$ and $\sim 300\,GeV$, using their conversion into an electron-positron pair, with the linear polarization affecting the azimuthal direction of the pair. Measuring this azimuthal direction is extremely challenging due to the multiple scattering of the electron-positron pair in the detector. We present the current effort to extract the polarization information from the $\textit{Fermi}$-LAT data, including recent developments in the simulation implementation and the event reconstruction and selection. This allows us to estimate the expected sensitivity to linear polarization of the $\textit{Fermi}$-LAT, and we apply this to the Vela pulsar.