The results of a dedicated search for pair production of scalar partners of charm quarks are reported. The search is based on an integrated luminosity of $20.3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of $pp$ collisions at $\sqrt{s}=8\text{ }\text{ }\mathrm{TeV}$ recorded with the ATLAS detector at the LHC. The search is performed using events with large missing transverse momentum and at least two jets, where the two leading jets are each tagged as originating from $c$ quarks. Events containing isolated electrons or muons are vetoed. In an $R$-parity-conserving minimal supersymmetric scenario in which a single scalar-charm state is kinematically accessible, and where it decays exclusively into a charm quark and a neutralino, 95% confidence-level upper limits are obtained in the scalar-charm--neutralino mass plane such that, for neutralino masses below 200 GeV, scalar-charm masses up to 490 GeV are excluded.