Global polarization of \(\Xi\) and \(\Omega\) hyperons has been measured for the first time in Au+Au collisions at \(\sqrt{s_{_{NN}}}\) = 200 GeV. The measurements of the \(\Xi^-\) and \(\bar{\Xi}^+\) hyperon polarization have been performed by two independent methods, via analysis of the angular distribution of the daughter particles in the parity violating weak decay \(\Xi\rightarrow\Lambda+\pi\), as well as by measuring the polarization of the daughter \(\Lambda\)-hyperon, polarized via polarization transfer from its parent. The polarization, obtained by combining the results from the two methods and averaged over \(\Xi^-\) and \(\bar{\Xi}^+\), is measured to be \(\langle P_\Xi \rangle = 0.47\pm0.10~({\rm stat.})\pm0.23~({\rm syst.})\,\%\) for the collision centrality 20\%-80\%. The \(\langle P_\Xi \rangle\) is found to be slightly larger than the inclusive \(\Lambda\) polarization and in reasonable agreement with a multi-phase transport model (AMPT). The \(\langle P_\Xi \rangle\) is found to follow the centrality dependence of the vorticity predicted in the model, increasing toward more peripheral collisions. The global polarization of \(\Omega\), \(\langle P_\Omega \rangle = 1.11\pm0.87~({\rm stat.})\pm1.97~({\rm syst.})\,\%\) was obtained by measuring the polarization of daughter \(\Lambda\) in the decay \(\Omega \rightarrow \Lambda + K\), assuming the polarization transfer factor \(C_{\Omega\Lambda}=1\).