In recent years, the collective motion properties of global rotation of the symmetric colliding system in relativistic energies have been investigated. In addition, the initial geometrical shape effects on the collective flows have been explored using a hydrodynamical model, a transport model, etc. In this work, we study the asymmetric $$^{12}{\mathrm {C}} + ^{197}\!\!\!{\mathrm{Au}}$$ 12C+197Au collision at $$200\,\hbox { GeV/}c$$ 200GeV/c and the effect of the exotic nuclear structure on the global rotation using a multi-phase transport model. The global angular momentum and averaged angular speed were calculated and discussed for the collision system at different evolution stages.