A search for gamma-ray bursts (GRBs) above 20 TeV within the field of view (1 sr) of the HEGRA AIROBICC Cherenkov array (29(deg) N, 18(deg) W, 2200 m a.s.l.) has been performed using data taken between March 1992 and March 1993. The search is based on an all-sky survey using four time scales, 10 seconds, 1 minute, 4 minutes and 1 hour. No evidence for TeV- emission has been found for the data sample. Flux upper limits are given. A special analysis has been performed for GRBs detected by BATSE and WATCH. Two partially and two fully contained GRBs in our field of view (FOV) were studied. For GRB 920925c which was fully contained in our FOV, the most significant excess has a probability of 7.7* 10(-8) (corresponding to 5.4sigma ) of being caused by a background fluctuation. Correcting this probability with the appropriate trial factor, yields a 99.7% confidence level (CL) for this excess to be related to the GRB (corresponding to 2.7sigma ). This result is discussed within the framework of the WATCH detection.