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