We report a new search for dark matter in a data sample of an integrated luminosity of 7.7 fb(-1) of Tevatron p (p) over bar collisions at root s = 1.96 TeV, collected by the CDF II detector. We search for production of a dark-matter candidate, D, in association with a single top quark. We consider the hadronic decay mode of the top quark exclusively, yielding a final state of three jets with missing transverse energy. The data are consistent with the standard model; we thus set 95% confidence level upper limits on the cross section of the process p (p) over bar -> t + D as a function of the mass of the dark-matter candidate. The limits are approximately 0.5 pb for a dark-matter particle with mass in the range of 0-150 GeV/c(2). RI maestro, paolo/E-3280-2010; song, hao/I-2782-2012