  Gravitational wave observations indicate the existence of merging black holes
(BHs) with high spin ($a\gtrsim0.3$), whose formation pathways are still an
open question. A possible way to form those binaries is through the tidal
spin-up of a Wolf-Rayet (WR) star by its BH companion. In this work, we
investigate this scenario by directly calculating the tidal excitation of
oscillation modes in WR star models, determining the tidal spin-up rate, and
integrating the coupled spin-orbit evolution for WR-BH binaries. We find that
for short-period orbits and massive WR stars, the tidal interaction is mostly
contributed by standing gravity modes, in contrast to Zahn's model of
travelling waves which is frequently assumed in the literature. The standing
modes are less efficiently damped than traveling waves, meaning that prior
estimates of tidal spin-up may be overestimated. We show that tidal
synchronization is rarely reached in WR-BH binaries, and the resulting BH spins
have $a \lesssim 0.4$ for all but the shortest period ($P_{\rm orb} \! \lesssim
0.5 \, {\rm d}$) binaries. Tidal spin-up in lower-mass systems is more
efficient, providing an anti-correlation between the mass and spin of the BHs,
which could be tested in future gravitational wave data. Nonlinear damping
processes are poorly understood but may allow for more efficient tidal spin-up.
We also discuss a new class of gravito-thermal modes that appear in our
calculations.
