Gamma-ray bursts (GRBs) are intense transient phenomena occurring at a rate of about one per day, and are considered promising candidate sources of cosmic neutrinos in the GeV-PeV energy range. Despite extensive efforts, no correlation between neutrinos and GRBs has been observed so far, motivating more exhaustive searches in a multi-messenger context.\\ In this contribution, a stacking search for neutrinos in spatial and time correlation of GRBs is presented, using data from the KM3NeT/ARCA detector. The detector, currently under construction at the bottom of the Mediterranean Sea, is already operational with partial configurations. This analysis employs data collected with the KM3NeT/ARCA 21 lines configuration, representing nearby $10\%$ of the complete detector. The search is based on methods originally developed for real-time analyses, incorporating refined calibrations, dynamic positioning and enhanced event selection criteria. No significant excess of candidate neutrino events coming from the population inspected of GRBs has been observed. The results include significance estimations from the GRB locations inspected, highlighting the potential of KM3NeT/ARCA to perform dedicated multi-messenger studies.