We predict the gamma-ray line emission from $r$-process nuclei synthesized in the ejecta of the accretion-induced collapse (AIC) of a magnetized, rapidly rotating white dwarf. Using ejecta from a two-dimensional general-relativistic neutrino-magnetohydrodynamic simulation, further evolved with a radiation-hydrodynamics code coupled to an in situ nuclear reaction network, we construct angle-dependent gamma-ray spectra in the 0.01–10 MeV band via composition-dependent ray tracing through the ejecta. The emission between $\sim 1$ and 10 d is dominated by ${}^{132}\mathrm{I}$ ($t_{1/2}=2.3\mathrm{h}$), continuously replenished by the decay of its parent ${}^{132}\mathrm{Te}$ ($t_{1/2}=3.2\mathrm{d}$), with additional contributions from ${}^{131}\mathrm{I}$, ${}^{133}\mathrm{Xe}$, and ${}^{132}\mathrm{Te}$. At $t\gtrsim 20\mathrm{d}$, ${}^{56}\mathrm{Co}$ (from ${}^{56}\mathrm{Ni}$ decay) becomes the primary emitter. The simultaneous presence of $r$ process and iron-peak gamma-ray lines is distinctive of AIC ejecta and absent in binary neutron star mergers, where iron-peak nuclei are generally not synthesized. Comparing with the $3\sigma$ continuum sensitivities of planned MeV gamma-ray telescopes (COSI, AMEGO-X, e-ASTROGAM, GRAMS, GammaTPC), we find the brightest $r$-process lines detectable to $\sim 10\mathrm{Mpc}$ by GammaTPC and GRAMS, with the signal approaching their sensitivity threshold at 30 Mpc. The $r$-process spectral features survive time integration over $\sim 30$ d exposures, demonstrating robustness against the long observation times required by gamma-ray detectors.