I had to change the car-turret setup and created a separate rigid body for the turret. So now I have 2 different rigid bodies, the car and the turret.
After going through the ConstraintDemo I came out with this:
// create constraint
btVector3 axisA(0.f, 1.f, 0.f);
btVector3 axisB(0.f, 0.f, 0.f);
btVector3 pivotA(0.f, 1.f, 0.f);
btVector3 pivotB(0.f, 0.f, 0.f);
hinge = new btHingeConstraint(*m_carChassis, *turretBody, pivotA, pivotB, axisA, axisB);
// add constraint to world
bt_dynamicsWorld->addConstraint(hinge, true);
I can now use hinge->enableAngularMotor(true, 0, 1);
to stop the turret rotation abdhinge->enableAngularMotor(true, angle, 1);
(float angle) to rotate it when I want to.