  We calculate the tidal response of a rotating black hole from the Teukolsky
equation in the near-horizon and small-frequency regime. While the static tidal
Love number of an arbitrarily rotating black hole is still zero, the dynamical
tidal Love number is not; rather, it is proportional to the angular velocity of
the black hole -- in the linear order of frequency -- and to the square of the
angular velocity of the black hole -- in the zeroth order. Intriguingly, the
zero-frequency limit of the dynamical tidal response function is not equal to
the static tidal response function. We demonstrate that these results hold true
for an extremal rotating black hole as well, with the dynamical tidal Love
numbers being non-zero. This shows that Kerr black holes experience dynamical
tides.
