  We study the transfer of angular momentum of guided photons to a two-level
atom with an electric quadrupole transition near an optical nanofiber. We show
that the generation of the axial orbital torque of the driving guided field on
the atom is governed by the internal-state selection rules for the quadrupole
transition and by the angular momentum conservation law with the photon angular
momentum given in the Minkowski formulation. We find that the torque depends on
the photon angular momentum, the change in the angular momentum of the atomic
internal state, and the quadrupole-transition Rabi frequency. We calculate
numerically the torques for the quadrupole transitions between the sublevel
$M=2$ of the hyperfine-structure level $5S_{1/2}F=2$ and the sublevels $M'=0$,
1, 2, 3, and 4 of the hyperfine-structure level $4D_{5/2}F'=4$ of a $^{87}$Rb
atom. We show that the absolute value of the torque for the higher-order mode
HE$_{21}$ is larger than that of the torque for the fundamental mode HE$_{11}$
except for the case $M'-M=2$, where the torque for the mode HE$_{21}$ is
vanishing.
