Для тех, кому это нужно, вот решение Магнуса в Swift:
func setAnchorPoint(anchorPoint: CGPoint, view: UIView) {
var newPoint: CGPoint = CGPointMake(view.bounds.size.width * anchorPoint.x, view.bounds.size.height * anchorPoint.y)
var oldPoint: CGPoint = CGPointMake(view.bounds.size.width * view.layer.anchorPoint.x, view.bounds.size.height * view.layer.anchorPoint.y)
newPoint = CGPointApplyAffineTransform(newPoint, view.transform)
oldPoint = CGPointApplyAffineTransform(oldPoint, view.transform)
var position: CGPoint = view.layer.position
position.x -= oldPoint.x
position.x += newPoint.x
position.y -= oldPoint.y
position.y += newPoint.y
view.setTranslatesAutoresizingMaskIntoConstraints(true) // Added to deal with auto layout constraints
view.layer.anchorPoint = anchorPoint
view.layer.position = position
}