The ipsocentric method at the coupled Hartree-Fock level is used for the calculation of magnetically induced ring currents in the boron buckyball B(80), for both I(h) and distorted T(h) geometries. A close similarity between the current patterns in boron and carbon buckyballs is noted, but with a higher current density in B(80). Paratropic currents on the pentagons are predominant in the boron buckyball, and the central NICS value is positive. These observations support the conclusion that B(80) should be considered (weakly) anti-aromatic. The largest orbital contributions to the ring currents in both molecules are identified and related to specific excitations in the frontier orbital region.