  Recent observations revealed a coherence between the spin vector of a galaxy
and the orbital motion of its neighbors. We refer to the phenomenon as "the
spin$-$orbit alignment (SOA)" and explore its physical origin via the
IllustrisTNG simulation. This is the first study to utilize a cosmological
hydrodynamic simulation to investigate the SOA of galaxy pairs. In particular,
we identify paired galaxies at $z = 0$ having the nearest neighbor with mass
ratios from 1/10 to 10 and calculate the spin$-$orbit angle for each pair. Our
results are as follows. (a) There exists a clear preference for prograde
orientations (i.e., SOA) for galaxy pairs, qualitatively consistent with
observations. (b) The SOA is significant for both baryonic and dark matter
spins, being the strongest for gas and the weakest for dark matter. (c) The SOA
is stronger for less massive targets and for targets having closer neighbors.
(d) The SOA strengthens for galaxies in low-density regions, and the signal is
dominated by central$-$satellite pairs in low-mass halos. (e) There is an
explicit dependence of the SOA on the duration of interaction with its current
neighbor. Taken together, we propose that the SOA witnessed at $z = 0$ has been
developed mainly by interactions with a neighbor for an extended period of
time, rather than tidal torque from the ambient large-scale structure.
