  Photons carry one unit of angular momentum associated with their
spin~\cite{Beth1936}. Structured vortex beams carry additional orbital angular
momentum which can also be transferred to matter~\cite{Allen1992}. This extra
twist has been used for example to drive motion of microscopic particles in
optical tweezers as well as to create vortices in degenerate quantum
gases~\cite{He1995,Andersen2006}. Here we demonstrate the transfer of optical
orbital angular momentum from the transverse spatial structure of the beam to
the internal (electronic) degrees of freedom of an atom. Probing a quadrupole
transition of a single trapped $^{40}$Ca$^+$ ion localized at the center of the
vortex, we observe strongly modified selection rules, accounting for both the
photon spin and the vorticity of the field. In particular, we show that an atom
can absorb two quanta of angular momentum from a single photon even when
rotational symmetry is conserved. In contrast to previous
findings~\cite{Araoka2005,Loeffler2011a,Mathevet2013}, our experiment allows
for conditions where the vorticity of the laser beam determines the optical
excitation, contributing to the long-standing discussion on whether the orbital
angular momentum of photons can be transferred to atomic internal degrees of
freedom~\cite{VanEnk1994,Babiker2002,Jauregui2004, Schmiegelow2012, Mondal2014,
Scholz-Marggraf2014} and paves the way for its use to tailor light-matter
interactions.
