Magnetic field sensing can be directly (i.e. without requiring magnetic fuilds or magnetostrictive materials) obtained from the estimation of the circular birefringence induced in optical fibers through the so-called Faraday effect. In standard telecommunication-grade optical fiber, the amount of induced circular birefringence is however of the same order of the intrinsic fiber linear birefringence or even below. Hence, whenever uniform fiber Bragg gratings (FBGs) are used to probe this evolution, the resulting accuracy is usually very poor, even in the case of polarization-assisted measurements based on polarization dependent loss (PDL) or differential group delay (DGD). In this work, we demonstrate that the rotation of the diattenuation vector computed from the Mueller matrix of an FBG in transmission mode can be efficiently used as a read-out technique to sense a magnetic field evolution with a resolution of 0.1T.