Massless Dirac fermions have been observed in various materials such as graphene and topological insulators in recent years, thus offering a solid-state platform to study relativistic quantum phenomena. Single quantum dots (QDs) and coupled QDs formed with massless Dirac fermions can be viewed as artificial relativistic atoms and molecules, respectively. Such structures offer a unique platform to study atomic and molecular physics in the ultra-relativistic regime. Here, we use a scanning tunneling microscope to create and probe single and coupled electrostatically defined graphene QDs to unravel the unique magnetic field responses of artificial relativistic nanostructures. Giant orbital Zeeman splitting and orbital magnetic moment up to ~70 meV/T and ~600𝜇 𝐵 are observed in single graphene QDs. While for coupled graphene QDs, Aharonov-Bohm oscillations and strong Van Vleck paramagnetic shift (~20 meV/T 2 ) are observed. Such properties of artificial relativistic atoms and molecules can be leveraged for novel magnetic field sensing modalities.