  We compute the spin-tidal couplings that affect the dynamics of two orbiting
bodies at the leading order in the post-Newtonian (PN) framework and to linear
order in the spin. These corrections belong to two classes: (i) terms arising
from the coupling between the ordinary tidal terms and the point-particle
terms, which depend on the standard tidal Love numbers of order $l$ and affect
the gravitational-wave (GW) phase at $(2l+5/2)$PN order and (ii) terms
depending on the rotational tidal Love numbers, recently introduced in previous
work, that affect the GW phase at $(2l+1/2+\delta_{2l})$PN order. For circular
orbits and spins orthogonal to the orbital plane, all leading-order spin-tidal
terms enter the GW phase at $1.5$PN order relative to the standard,
quadrupolar, tidal deformability term (and, thus, before the standard octupolar
tidal deformability terms). We present the GW phase that includes all tidal
terms up to $6.5$PN order and to linear order in the spin. We comment on a
conceptual issue related to the inclusion of the rotational tidal Love numbers
in a Lagrangian formulation and on the relevance of spin-tidal couplings for
parameter estimation in coalescing neutron-star binaries and for tests of
gravity.
