We present a model for the seeding and evolution of magnetic fields in protogalaxies. Supernova (SN) explosions during the assembly of a protogalaxy provide magnetic seed fields, which are subsequently amplified by compression, shear flows and random motions. We implement the model into the MHD version of the cosmological N-body / SPH simulation code GADGET and we couple the magnetic seeding directly to the underlying multi-phase description of star formation. We perform simulations of Milky Way-like galactic halo formation using a standard LCDM cosmology and analyse the strength and distribution of the subsequent evolving magnetic field. A dipole-shape divergence-free magnetic field is injected at a rate of 10^{-9}G / Gyr within starforming regions, given typical dimensions and magnetic field strengths in canonical SN remnants. Subsequently, the magnetic field strength increases exponentially on timescales of a few ten million years. At redshift z=0, the entire galactic halo is magnetized and the field amplitude is of the order of a few $μ$G in the center of the halo, and 10^{-9} G at the virial radius. Additionally, we analyse the intrinsic rotation measure (RM) of the forming galactic halo over redshift. The mean halo intrinsic RM peaks between redshifts z=4 and z=2 and reaches absolute values around 1000 rad m^{-2}. While the halo virializes towards redshift z=0, the intrinsic RM values decline to a mean value below 10 rad m^{-2}. At high redshifts, the distribution of individual starforming, and thus magnetized regions is widespread. In our model for the evolution of galactic magnetic fields, the seed magnetic field amplitude and distribution is no longer a free parameter, but determined self-consistently by the star formation process occuring during the formation of cosmic structures. ; Comment: 13 pages, 14 figures, accepted to MNRAS after moderate revision