The first relevant passage is Deut. 17: 14-20: "When you come to the land which Yahweh your Elohim is giving you, and possess it and dwell in it, and say, 'I will set a king over me like all the nations that are around me,' you shall surely set a king over you whom Yahweh your Elohim chooses; one from among your brethren you shall set as king over you; you may not set a foreigner over you, who is not your brother. [...]" (Please read verses 16-20 for yourself.)
"Then all the elders of Israel gathered together and came to Samuel at Ramah, and said to him, "Look, you are old, and your sons do not walk in your ways. Now make us a king to judge us like all the nations." But the thing displeased Samuel when they said, "Give us a king to judge us." So Samuel prayed to Yahweh. And Yahweh said to Samuel, "Heed the voice of the people in all that they say to you; for they have not rejected you, but they have rejected Me, that I should not reign over them. According to all the works which they have done since the day that I brought them up out of Egypt, even to this day -- with which they have forsaken Me and served other gods -- so they are doing to you also. Now therefore, heed their voice. However, you shall solemnly forewarn them the behavior of the king who will reign over them."
So Samuel told all the words of Yahweh to the people who asked him for a king. And he said, "[...] He will take a tenth of your sheep. And you will be his servants. And you will cry out in that day because of your king whom you have chosen for yourselves, and Yahweh will not hear you in that day."
Nevertheless the people refused to obey the voice of Samuel; and they said, "No, but we will have a king over us, that we may also be like all the nations, and that our king may judge us and go out before us and fight our battles." [...] So Yahweh said to Samuel, "Heed their voice, and make them a king."
Israel is as stiffnecked now as ever before. At that time they rejected Yahweh as their king, but at least they still trusted Yahweh's prophet to choose their king. Even so, Yahweh considered this as the people rejecting Him as their King. Now the people in all democracies all over the world choose their leaders (President, members of Parliament, ...) themselves. They wouldn't even dream of letting a prophet or servant of Yahweh choose their President. So they organize Presidential elections.
By taking part in such elections, each voter individually approves of this election system, and thus personally rejects Yahweh as King. Yahweh's promise to these voters is: "You will cry out in that day because of your king whom you have chosen for yourselves, and Yahweh will not hear you in that day."
The only way to show that you want Yahweh as your King, is by not participating in this worldly election system. Be NOT conformed to this world!
"Come out of her, my people, lest you share in her sins, and lest you receive of her plagues. For her sins have reached to heaven" (Rev. 18: 4-5).