By using high-resolution spectra acquired with FLAMES-GIRAFFE at the ESO/ VLT, we measured the radial and rotational velocities for 110 blue straggler stars (BSSs) in omega Centauri, the globular cluster-like stellar system harboring the largest known BSS population. According to their radial velocities, 109 BSSs are members of the system. The rotational velocity distribution is very broad, with the bulk of BSSs spinning at less than similar to 40 km s(-1) (in agreement with the majority of such stars observed in other globular clusters) and a long tail reaching similar to 200 km s(-1). About 40% of the sample has v(e) sin i > 40 km s(-1) and about 20% has ve sin i > 70 km s(-1). Such a large fraction is very similar to the percentage of fast rotating BSSs observed in M4. Thus, omega Centauri is the second stellar cluster, beyond M4, with a surprisingly high population of fast spinning BSSs. We found a hint of radial behavior for a fraction of fast rotating BSSs, with a mild peak within one core radius, and a possible rise in the external regions (beyond four core radii). This may suggest that recent formation episodes of mass transfer BSSs occurred preferentially in the outskirts of omega Centauri, or that braking mechanisms able to slow down these stars are least efficient in the lowest density environments.