Put simply, he picked it up off the ground after River left it there, presumably on his instruction.
There is a scene in "The Pandorica Opens", right before the Doctor gives his big speech to the aliens that are descending on Stonehenge, which shows River on a horse asking the Doctor (via communicator) if he has a plan. It then shows the Doctor on the ground next to the Pandorica, scanning it with his sonic screwdriver. Right next to his head, the vortex manipulator can be clearly seen.
This is followed up on in "The Big Bang", when the Doctor is shown picking the manipulator up after being let out by the Auton copy of Rory, which he then uses to jump ahead from 102 A.D. to the museum in the 1990s.