Two searches are conducted for muon neutrinos from Gamma-Ray Bursts (GRBs) using the IceCube detector. Gamma-Ray Bursts are brief and transient emissions of keV/MeV radiation occuring with a rate of a few per day uniformly in the sky. Swift and other satellites of the Third Interplanetary Network (IPN3) detect these GRBs and send notices out via the GRB Coordinate Network (GCN). The fireball model describing the physics of GRBs predicts the emission of muon neutrinos from these bursts. IceCube is a cubic kilometer neutrino detector buried in the deep antarctic ice at the South Pole that can be used to find these prediceted but still unobserved neutrinos. It is sensitive to them by detecting Cherenkov light from secondary muons produced when the neutrinos interact in or near the instrumented volume. The construction of IceCube has been underway since the austral summer of 2004-2005 and will continue until 2011. The growing IceCube detector will soon be sensitivite to the high energy neutrino emission from GRBs that is predicted by the fireball model. A blind and triggered search of the 22-string IceCube data for this neutrino emission was conducted. The principal background to the observation of neutrinos in IceCube is muons generated in cosmic-ray air-showers in the atmosphere above the detector. Atmospheric neutrinos make up a separate irreducible background to the detection of extraterrestrial neutrinos. A binned stacked search of 41 bursts occuring in the northern hemisphere greatly reduces the muon background by looking for tracks moving up through the detector. The atmospheric neutrino background is greatly reduced by the temporal constraints of the search, making it effectively background free. 40 individual unbinned searches of bursts occuring in the southern hemisphere extend IceCube's sensitivity to the higher background regions above the horizon. No significant excesses over background expectations are found in either search. A 90% confidence upper limit on the neutrino fluence from northern hemisphere bursts is set at 6.52 x 10-3 erg cm-2 with 90% of the expected signal between 87.9 TeV and 10.4 PeV.