  We report the results of a search for inelastic scattering of weakly
interacting massive particles (WIMPs) off $^{127}$I nuclei using NaI(Tl)
crystals with a data exposure of 97.7 kg$\cdot$years from the COSINE-100
experiment. The signature of inelastic WIMP-$^{127}$I scattering is a nuclear
recoil accompanied by a 57.6 keV $\gamma$-ray from the prompt deexcitation,
producing a more energetic signal compared to the typical WIMP nuclear recoil
signal. We found no evidence for this inelastic scattering signature and set a
90 $\%$ confidence level upper limit on the WIMP-proton spin-dependent,
inelastic scattering cross section of $1.2 \times 10^{-37} {\rm cm^{2}}$ at the
WIMP mass 500 ${\rm GeV/c^{2}}$.
