  Gravitational waves from neutron star binary inspirals contain information on
strongly-interacting matter in unexplored, extreme regimes. Extracting this
requires robust theoretical models of the signatures of matter in the
gravitational-wave signals due to spin and tidal effects. In fact, spins can
have a significant impact on the tidal excitation of the quasi-normal modes of
a neutron star, which is not included in current state-of-the-art waveform
models. We develop a simple approximate description that accounts for the
Coriolis effect of spin on the tidal excitation of the neutron star's
quadrupolar and octupolar fundamental quasi-normal modes and incorporate it in
the SEOBNRv4T waveform model. We show that the Coriolis effect introduces only
one new interaction term in an effective action in the co-rotating frame of the
star, and fix the coefficient by considering the spin-induced shift in the
resonance frequencies that has been computed numerically for the mode
frequencies of rotating neutron stars in the literature. We investigate the
impact of relativistic corrections due to the gravitational redshift and
frame-dragging effects, and identify important directions where more detailed
theoretical developments are needed in the future. Comparisons of our new model
to numerical relativity simulations of double neutron star and neutron
star-black hole binaries show improved consistency in the agreement compared to
current models used in data analysis
