Recent publications by Contopoulos and collaborators provided the structure of black hole magnetospheres. These works have shown their close analogy with the well studied pulsar mangetospheres, including the presence of (two) light cylinders and the global current closure through current sheets. Just as in pulsars, the structure of the magnetosphere determines the charge of the current sheet to be positive (provided the magnetic field direction aligns with that of the black hole spin). While in pulsars the necessary positive current sheet charges are produced by e+e- pair production, in AGN they can be provided by the accretion disk protons. We show that these can be accelerated in the current sheet to energies sufficiently large to produce, through interactions with the accretion disk photons, the neutrinos observed in Ice Cube.