The Major Atmospheric Gamma Imaging Cherenkov (MAGIC) telescope was designed for the detection of photon sources >~50 GeV. The measurement of highly-inclined air showers renders possible the search for high-energy neutrinos, too. Only neutrinos can traverse the Earth without interaction, and therefore, events close to the horizon can be identified as neutrino-induced rather than photon-induced or hadronic events. In this paper, Swift-XRT-detected GRBs with given spectral information are used in order to calculate the potential neutrino energy spectrum from prompt and afterglow emission for each individual GRB. The event rate in MAGIC is estimated assuming that the GRB happens within the field of view of MAGIC. A sample of 568 long GRBs as detected by BATSE is used to compare the detection rates with 163 Swift-detected bursts. BATSE has properties similar to the Gamma-ray Burst Monitor (GBM) on board of GLAST. Therefore the estimated rates give an estimate for the possibilities of neutrino detection with MAGIC from GLAST-triggered bursts.