Large-scale coherent magnetic fields are observed in galaxies and clusters, but their ultimate origin remains a mystery. We reconsider the prospects for primordial magnetogenesis by a cosmic string network. We show that the magnetic flux produced by long strings has been overestimated in the past, and give improved estimates. We also compute the fields created by the loop population, and find that it gives the dominant contribution to the total magnetic field strength on present-day galactic scales. We present numerical results obtained by evolving semi-analytic models of string networks (including both one-scale and velocity-dependent one-scale models) in a Lambda-CDM cosmology, including the forces and torques on loops from Hubble redshifting, dynamical friction, and gravitational wave emission. Our predictions include the magnetic field strength as a function of correlation length, as well as the volume covered by magnetic fields. We conclude that string networks could account for magnetic fields on galactic scales, but only if coupled with an efficient dynamo amplification mechanism.