  The MAGIC telescopes, located at the Roque de los Muchachos Observatory (2200
a.s.l.) in the Canary Island of La Palma, are placed on the top of a mountain,
from where a window of visibility of about 5 deg in zenith and 80 deg in
azimuth is open in the direction of the surrounding ocean. This permits to
search for a signature of particle showers induced by earth-skimming cosmic tau
neutrinos in the PeV to EeV energy range arising from the ocean. We have
studied the response of MAGIC to such events, employing Monte Carlo simulations
of upward-going tau neutrino showers. The analysis of the shower images shows
that air showers induced by tau neutrinos can be discriminated from the
hadronic background coming from a similar direction. We have calculated the
point source acceptance and the expected event rates, assuming an incoming tau
neutrino flux consistent with IceCube measurements, and for a sample of generic
neutrino fluxes from photo-hadronic interactions in AGNs. The analysis of about
30 hours of data taken toward the sea leads to a point source sensitivity for
tau neutrinos at the level of the down-going point source analysis of the
Pierre Auger Observatory.
