Abstract: Gamma-ray bursts (GRBs) are among the most luminous electromagnetic events in the universe. These are divided into two subtypes: long GRBs (LGRBs), originating from the collapse of massive stars with a typical duration exceeding two seconds, and short GRBs, associated with the merger of binary compact objects. LGRBs at high redshifts serve as key indicators of star formation during the early stages of cosmic reionization, driven by the first Population III (Pop III) stars. The rate of GRBs from isolated Pop III stars remains uncertain due to limited knowledge of their initial mass function, rotation, stellar evolution, and mass loss. Massive Pop III stars undergoing core-collapse may produce relativistic jets that power GRBs. In the collapsar model, rapid progenitor rotation and minimal mass loss are crucial for sufficient angular momentum transfer to the remnant black hole. In this work, we analyse a grid of Pop III stellar evolution models with initial masses between 20 and 100 solar masses and initial rotation rates between 60 and 90% of critical rotation. Using a realistic accretion model, we calculate the whole masses, spins, and evolution of black holes and their disks. A semi-analytical approach models jet propagation and breakout through the stellar envelope, enabling us to estimate GRB production efficiency based on progenitor mass, rotation, and wind efficiency. Compared to the observed high-redshift GRB rates so far, we conclude that isolated Pop III stars cannot produce detectable GRBs by current detectors. If they are observed, they most likely originate from binary stellar systems instead.