The interplay of strong interactions and magnetic fields gives rise to unusual forms of superconductivity and magnetism in quantum many-body systems. Here, we present an experimental study of the two-dimensional Fermi-Hubbard model—a paradigm for strongly correlated fermions on a lattice—in the presence of a Zeeman field and varying doping. Using site-resolved measurements, we revealed anisotropic antiferromagnetic correlations, a precursor to long-range canted order. We observed nonmonotonic behavior of the local polarization with doping for strong interactions, which we attribute to the evolution from an antiferromagnetic insulator to a metallic phase. Our results pave the way to experimentally mapping the low-temperature phase diagram of the Fermi-Hubbard model as a function of both doping and spin polarization, for which many open questions remain.