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 experimental design allows for highly efficient detection of photon-induced air showers in the TeV and sub-TeV range and gamma-hadron separation. We show that HAWC has a reasonable chance to observe the high-energy power law components of GRBs that extend to 50 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. An engineering array consisting of 6 water tanks was operated at the HAWC site since September 2011, collecting 3 months of data. An upper limit on high energy emission from GRB 111016B is derived from these data.