  Primordial black holes (PBHs) are known as one of the potential candidates
for dark matter. They are expected to have formed due to the direct
gravitational collapse of density fluctuations in the early Universe.
Therefore, the study of the merger rate of PBHs in modified theories of gravity
can provide more detailed information about their abundance. In this work, we
delve into the calculation of the merger rate of PBHs within the theoretical
framework of $f(R)$ gravity. Our analysis reveals an enhancement in the merger
rate of PBHs compared to that obtained from general relativity (GR).
Additionally, modulating the field strength $f_{R0}$ induces shifts in the PBH
merger rate, presenting a potential observational signature of modified
gravity. We also find that the total merger rate of PBHs will be consistent
with the merger rate of black holes estimated by the Laser Interferometer
Gravitational-Wave Observatory (LIGO)-Virgo-KAGRA detectors if $f_{PBH}\gtrsim
0.1$. While further improvements might be required, relative enhancement of the
merger rate of PBHs in the framework of $f(R)$ gravity and its consistency with
gravitational wave data underscore the importance of employing modified
theories of gravity to examine diverse scenarios related to the formation of
black holes.
