  We demonstrate the excitation, using a structured light beam carrying orbital
angular momentum, of the center of mass motion of a single atom in the
transverse direction to the beam's propagation. This interaction is achieved
with a vortex beam carrying one unit of orbital angular momentum and one unit
of spin/polarization angular momentum. Using a singly charged $^{40}$Ca$^+$
ion, cooled near the ground state of motion in the 3D harmonic potential of a
Paul trap, we probe the narrow S$_{1/2}$ to D$_{5/2}$ transition near
$729\,\mathrm{nm}$ on its motional sidebands to quantify the momentum transfer.
Exchange of quanta in the perpendicular direction to the beam's wave vector
$\mathbf{k}$ is observed in case of the vortex shaped beam, in strong contrast
to the absence of this spin-motion coupling for the case of a Gaussian beam. We
characterize the coherent interaction by an effective transverse Lamb-Dicke
factor $\eta^\mathrm{exp}_{\perp}=0.0062(5)$ which is in agreement with our
theoretical prediction $\eta^\mathrm{theo}_{\perp}=0.0057(1)$
