Excited states in ${}^{234}\mathrm{U}$ have been populated using the incomplete-fusion reaction ${}^{232}\mathrm{Th}{(}^{9}\mathrm{Be},\ensuremath{\alpha}3n)$ at 52 MeV. The emitted $\ensuremath{\gamma}$ rays were observed using the CAESAR array, while the $\ensuremath{\alpha}$ particles were detected with an array of 14 plastic scintillator detectors of phoswich type. This reaction can populate ${}^{234}\mathrm{U}$ at higher spin than the conventional ${}^{232}$Th$(\ensuremath{\alpha},$ $2n)$ reaction because the ``${}^{5}\mathrm{He}$'' fragment from breakup of the beam can be viewed as initiating a ${}^{232}\mathrm{Th}{(}^{5}\mathrm{He},3n)$ reaction. Similar reactions could provide a valuable alternative technique for the study of relatively heavy, neutron-rich isotopes. In the present work, states in the ground-state band of ${}^{234}\mathrm{U}$ were observed up to ${J}^{\ensuremath{\pi}}{=18}^{+}$ and previous tentative observations of ${(9}^{\ensuremath{-}})$ and ${(11}^{\ensuremath{-}})$ states in the octupole band were confirmed. A new state at 1366 keV, which is possibly the ${8}^{+}$ member of the $\ensuremath{\gamma}$ band, has also been identified.