We present a search for the pair production of scalar top quarks, $\tilde{t}$, using 995 pb$^{-1}$ of data collected in $p\bar{p}$ collisions with the D0 detector at the Fermilab Tevatron Collider at $\sqrt{s} = 1.96$ TeV. Both scalar top quarks are assumed to decay into a charm quark and a neutralino ($\tilde{\chi}^{0}_{1}$), where $\tilde{\chi}^{0}_{1}$ is the lightest supersymmetric particle. This leads to a final state with two acoplanar charm jets and missing transverse energy. We find the yield of such events to be consistent with the standard model expectation, and exclude sets of $\tilde{t}$ and $\tilde{\chi}^{0}_{1} $ masses at the 95% C.L. that substantially extend the domain excluded by previous searches.