We report on the induction of magnetization in Rydberg systems by means of the inverse Faraday effect and propose the appearance of the effect in two such systems: Rydberg atoms proper and shallow dopants in semiconductors. Rydberg atoms are characterized by a large orbital radius. This large radius gives such excited states a large angular moment, which when driven with circularly polarized light translates to a large effective magnetic field Beff. We calculate this effect to generate effective magnetic fields of O (1 mu T) x( 1 omega THz )-1( I 10 W cm-2 )n4 in the Rydberg states of atoms such as Rb and Cs for off-resonant photon beams with frequency omega and intensity I expressed in units of the denominators and n the principal quantum number. Additionally, terahertz spectroscopy of phosphorus-doped silicon reveals a large cross section for excitation of shallow dopants to Rydberg-like states, which even for small n have the potential to be driven similarly with circularly polarized light to produce an even larger magnetization. Our theoretical calculations estimate Beff as O(102 T) for Si:P with a beam intensity of 108 W cm-2.