The High Altitude Water Cherenkov Observatory (HAWC) is an air shower array currently under construction in Mexico at an altitude of 4100 m. HAWC will consist of 300 large water tanks covering an area of about 22000 square meters and instrumented with 4 photomultipliers each. The array is sensitive to photon-induced air showers in the TeV and sub-TeV range and provides gamma-hadron separation capabilities. We show that HAWC has a realistic opportunity to observe the high-energy power law components of GRBs that extend at least up to 30 GeV. In particular, HAWC will be capable of observing events similar to GRB 090510 and GRB 090902b. The observations (or non-observations) of GRBs by HAWC will provide information on the high-energy spectra of GRBs. A small array of water tanks was operated at the HAWC site in 2011 and 2012. The collected data were used to set an upper limit on high energy emission from GRB 111016b.