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By using a method improved with a generalized optical metric, the deflectionof light for an observer and source at finite distance from a lens object in astationary, axisymmetric and asymptotically flat spacetime has been recentlydiscussed [Ono, Ishihara, Asada, Phys. Rev. D {\bf 96}, 104037 (2017)]. In thispaper, we study a possible extension of this method to an asymptoticallynonflat spacetime. We discuss a rotating global monopole. Our result of thedeflection angle of light is compared with a recent work on the same spacetimebut limited within the asymptotic source and observer [Jusufi et al., Phys.Rev. D {\bf 95}, 104012 (2017)], in which they employ another approach proposedby Werner with using the Nazim's osculating Riemannian construction method viathe Randers-Finsler metric. We show that the two different methods give thesame result in the asymptotically far limit. We obtain also the corrections tothe deflection angle due to the finite distance from the rotating globalmonopole. Near-future observations of Sgr A${}^{*}$ will be able to put a boundon the global monopole parameter $\beta$ as $1- \beta < 10^{-3}$ for a rotatingglobal monopole model, which is interpreted as the bound on the deficit angle$\delta < 8\times 10^{-4}$ [rad].

Deflection angle of light for an observer and source at finite distance from a rotating global monopole