  The black holes that have been detected via gravitational waves (GW) can have
either astrophysical or primordial origin. Some GW events show significant spin
for one of the components and have been assumed to be astrophysical, since
primordial black holes are generated with very low spins. However, it is worth
studying if they can increase their spin throughout the evolution of the
universe. Possible mechanisms that have already been explored are multiple
black hole mergers and gas accretion. We propose here a new mechanism that can
occur in dense clusters of black holes: the spin-up of primordial black holes
when they are involved in close hyperbolic encounters. We explore this effect
numerically with the Einstein Toolkit for different initial conditions,
including variable mass ratios. For equal masses, there is a maximum spin that
can be induced on the black holes, $\chi = a/m \leq 0.2$. We find however that
for large mass ratios one can attain spins up to $\chi \simeq 0.8$, where the
highest spin is induced on the most massive black hole. For small induced spins
we provide simple analytical expressions that depend on the relative velocity
and impact parameter.
