  We used high resolution spectra acquired at the Magellan Telescope to measure
radial and rotational velocities of approximately 200 stars in the Galactic
globular cluster NGC 3201. The surveyed sample includes Blue Stragglers Stars
(BSSs) and reference stars in different evolutionary stages (main sequence
turn-off, sub-giant, red giant and asymptotic giant branches). The average
radial velocity value ($\langle V_r\rangle = 494.5 \pm 0.5$ km s$^{-1}$)
confirms a large systemic velocity for this cluster and was used to distinguish
33 residual field interlopers. The final sample of member stars counts 67 BSSs
and 114 reference stars. Similarly to what is found in other clusters, the
totality of the reference stars has negligible rotation ($<20$ km s$^{-1}$),
while the BSS rotational velocity distribution shows a long tail extending up
to $\sim 200$ km s$^{-1}$, with 19 BSSs (out of 67) spinning faster than 40 km
s$^{-1}$. This sets the percentage of fast rotating BSSs to $\sim 28\%$. Such a
percentage is roughly comparable to that measured in other loose systems
($\omega$ Centauri, M4 and M55) and significantly larger than that measured in
high-density clusters (as 47 Tucanae, NGC 6397, NGC 6752 and M30). This
evidence supports a scenario where recent BSS formation (mainly from the
evolution of binary systems) is occurring in low-density environments. We also
find that the BSS rotational velocity tends to decrease for decreasing
luminosity and surface temperature, similarly to what is observed in main
sequence stars. Hence, further investigations are needed to understand the
impact of BSS internal structure on the observed rotational velocities.
