We derive general universal scaling relations governing resonances induced by the dipole moment of excited positronium interacting with atomic ions. A single non-universal parameter, which contains all the system-dependent information, is defined. Our results are compared to numerical calculations, using complex scaling, for S, P, and D-wave resonances below the positronium n. =. 2 threshold in the e(+)-(H, Li, Na, K) systems. The energy and width ratios of the successive resonances are found to agree well with the analytically derived scaling law.