We present VLT FLAMES spectroscopic observations (R~6500) in the Ca II triplet region for 470 probable kinematic members of the Sculptor (Scl) dwarf spheroidal galaxy. The accurate velocities (+/-2 km s-1) and large area coverage of Scl allow us to measure a velocity gradient of 7.6+3.0-2.2 km s-1 deg-1 along the projected major axis of Scl, likely a signature of intrinsic rotation. We also use our kinematic data to measure the mass distribution within this system. By considering independently the kinematics of the two distinct stellar components known to be present in Scl, we are able to relieve known degeneracies and find that the observed velocity dispersion profiles are best fitted by a cored dark matter halo with core radius rc=0.5 kpc and mass enclosed within the last measured point M(<1.8 kpc) = (3.4 +/- 0.7) × 108 Msolar, assuming an increasingly radially anisotropic velocity ellipsoid. This results in a mass-to-light ratio of 158 +/- 33 (M/L)solar inside 1.8 kpc. An NFW profile with concentration c=20 and mass M(<1.8 kpc) = 2.2+1.0-0.7×108 Msolar is also statistically consistent with the observations, but it tends to yield poorer fits for the metal-rich stars. Based on FLAMES observations collected at the ESO, proposals 171.B-0588 and 076.B-0391A.