I can't think of a Scripture passage that encourages it.
Moses was a government official until he wasn't; there was no way to change things within the government. One could cite Joseph but then his influence waned until we end up with the subjugation of God's people and the need for a Moses to come forth.
All of the kings from Saul onward were not God's plan (Yahweh was to be the Most High but the people of Israel wanted a human leader, Samuel reluctantly offered one (David): and the people chose otherwise (Saul).). David and Solomon were flawed although remembered as the archetypal kingly leaders. Most of the prophets were counterpoints to political leadership; all of them were correctives to the flawed political leadership of the kings.
Every one of the Proverbs that refers to avoiding deceit and seeking humility, both contrary to Machiavellian political methods.
John the Baptist and Jesus who both challenged secular authority and paid with their lives. Paul engaged political authority only so far as to move forward the reign of God but never as an active participant. John the Baptist, Jesus, and Paul were all at some point in their ministries considered lawbreakers and criminals by the state authority. From the Gospels, I think of Nicodemus as a political leader who was disappointed that Jesus did not try to change the government by the usual means.
Just a few thoughts about why I hold my opinion about the difficulty, well, the impossibility of faithful Christian believers holding political office.
Should Christians participate in the political process? Sure. Go vote, challenge the status quo, and support causes. Be an activist. I just believe the Christian voice is more effective as a counselor and prophet than as an office holder.