The righteous scepter of the King of the kingdom of God – who is, of course, Jesus our Lord – is the life He lived on earth.
A rod is a branch that is cut off from the tree. And, of course, Jesus was the Branch (Isaiah 4:2 and elsewhere) and He was cut off from the living (Isaiah 53:8).
Jesus lived a perfect life. He loved everyone – even His enemies. He turned the other cheek; He walked the extra mile. To put it succinctly, He practiced what He preached. That perfect life was cut short (“cut off”).
It is by this life that He measures righteousness. If you want to be righteous, measure up to that.
Scripture quotations taken from the NASB, unless otherwise noted.