We set the first limits on the ultra-high energy (UHE) neutrino fluence at energies greater than 10^9 GeV from gamma-ray bursts (GRBs) based on data from the second flight of the ANtarctic Impulsive Transient Antenna (ANITA). During the 31 day flight
of ANITA-II, 26 GRBs were recorded by Swift or Fermi. Of these, we analyzed the 12 GRBs which occurred during quiet periods when the payload was away from anthropogenic activity. In a blind analysis, we observe 0 events on a total background of 0.0044 events in the combined prompt window for all 12 low-background bursts. We also observe 0 events from the remaining 14 bursts. We place a 90% confidence level limit on the E^-4 prompt neutrino fluence of 2.5x10^17 GeV^3/cm^2 between 10^8 and 10^12 GeV from GRB090107A. This is the first reported limit on the UHE neutrino fluence from GRBs above 10^9 GeV, and the strongest limit above 10^8 GeV.
