  We investigate the absorption properties of reflection-asymmetric wormholes
constructed via the thin-shell formalism in Palatini $f({\cal R})$ gravity.
Such wormholes come from the matching of two Reissner-Nordstr\"om spacetimes at
a time-like hypersurface (shell), which, according to the junction conditions
in Palatini $f({\cal R})$ gravity, can have positive or negative energy
density. Using numerical methods we investigate several configurations that
satisfy the junction conditions, and analyze how the parameters of the system
affect the absorption spectra. We confirm that the absorption cross section of
wormholes at low frequencies significantly departs from that of black holes,
and observe that in configurations made out of two naked singularities, the
absorption spectra exhibit new features due to the effective light ring
associated to the wormhole throat. The possibility of observing the presence of
resonances at high frequencies is also discussed.
