  The radial velocity method is amongst the most robust and most established
means of detecting exoplanets. Yet, it has so far failed to detect circumbinary
planets despite their relatively high occurrence rates. Here, we report
velocimetric measurements of Kepler-16A, obtained with the SOPHIE spectrograph,
at the Observatoire de Haute-Provence's 193cm telescope, collected during the
BEBOP survey for circumbinary planets. Our measurements mark the first radial
velocity detection of a circumbinary planet, independently determining the mass
of Kepler-16~(AB)~b to be $0.313 \pm 0.039\,{\rm M}_{\rm Jup}$, a value in
agreement with eclipse timing variations. Our observations demonstrate the
capability to achieve photon-noise precision and accuracy on single-lined
binaries, with our final precision reaching $\rm 1.5~m\,s^{-1}$ on the binary
and planetary signals. Our analysis paves the way for more circumbinary planet
detections using radial velocities which will increase the relatively small
sample of currently known systems to statistically relevant numbers, using a
method that also provides weaker detection biases. Our data also contain a
long-term radial velocity signal, which we associate with the magnetic cycle of
the primary star.
