  The typical detection rate of $\sim1$ gamma-ray burst (GRB) per day by the
\emph{Fermi} Gamma-ray Burst Monitor (GBM) provides a valuable opportunity to
further our understanding of GRB physics. However, the large uncertainty of the
\emph{Fermi} localization typically prevents rapid identification of
multi-wavelength counterparts. We report the follow-up of 93 \emph{Fermi} GRBs
with the Gravitational-wave Optical Transient Observer (GOTO) prototype on La
Palma. We selected 53 events (based on favourable observing conditions) for
detailed analysis, and to demonstrate our strategy of searching for optical
counterparts. We apply a filtering process consisting of both automated and
manual steps to 60\,085 candidates initially, rejecting all but 29, arising
from 15 events. With $\approx3$ GRB afterglows expected to be detectable with
GOTO from our sample, most of the candidates are unlikely to be related to the
GRBs. Since we did not have multiple observations for those candidates, we
cannot confidently confirm the association between the transients and the GRBs.
Our results show that GOTO can effectively search for GRB optical counterparts
thanks to its large field of view of $\approx40$ square degrees and its depth
of $\approx20$ mag. We also detail several methods to improve our overall
performance for future follow-up programs of \emph{Fermi} GRBs.
