Does God select national leaders?  Let’s take a look at what the Bible says.

The prophet Daniel clearly states that God removes kings and raises up kings.

Dan 2:20  Daniel answered and said: “Blessed be the name of God forever and ever, For wisdom and might are His.
Dan 2:21  And He changes the times and the seasons; He removes kings and raises up kings; He gives wisdom to the wise And knowledge to those who have understanding.

This is repeated in a vision God gave king Nebuchadnezzar.

Dan 4:17  ‘This decision is by the decree of the watchers, And the sentence by the word of the holy ones, In order that the living may know That the Most High rules in the kingdom of men, Gives it to whomever He will, And sets over it the lowest of men.’

It is interesting to note that God sets over the kingdom of men the lowest men.  An example being king Nebuchadnezzar who was far from righteous as evidenced by Daniel advising the king to stop sinning so that he might live longer.

Dan 4:27  Therefore, O king, let my advice be acceptable to you; break off your sins by being righteous, and your iniquities by showing mercy to the poor. Perhaps there may be a lengthening of your prosperity.”

A similar sentiment of God of putting down one and exalting another is found in Psalms, which could be applied to leaders.

Psa 75:6  For exaltation comes neither from the east Nor from the west nor from the south.
Psa 75:7  But God is the Judge: He puts down one, And exalts another.

Some might argue that this only apples to king Nebuchadnezzar; however, we know that God also raised up Pharaoh of the Exodus and the Persian king Cyrus.

Exo 9:16  But indeed for this purpose I have raised you up, that I may show My power in you, and that My name may be declared in all the earth.

Isa 44:28  Who says of Cyrus, ‘He is My shepherd, And he shall perform all My pleasure, Saying to Jerusalem, “You shall be built,” And to the temple, “Your foundation shall be laid.” ‘
Isa 45:1  “Thus says the LORD to His anointed, To Cyrus, whose right hand I have held— To subdue nations before him And loose the armor of kings, To open before him the double doors, So that the gates will not be shut:

However, it does appear that at times God allows people to select their own leaders.

Hos 8:3  Israel has rejected the good; The enemy will pursue him.
Hos 8:4  “They set up kings, but not by Me; They made princes, but I did not acknowledge them. From their silver and gold They made idols for themselves— That they might be cut off.

There are a couple of passages in the New Testament which add to our understanding.  Jesus said that Pilate’s power had been given to him by God.

Joh 19:10  Then Pilate said to Him, “Are You not speaking to me? Do You not know that I have power to crucify You, and power to release You?”
Joh 19:11  Jesus answered, “You could have no power at all against Me unless it had been given you from above. Therefore the one who delivered Me to you has the greater sin.”

The apostle Paul expounds on this statement of Jesus a little bit.

Rom 13:1  Let every soul be subject to the governing authorities. For there is no authority except from God, and the authorities that exist are appointed [tasso] by God.
Rom 13:2  Therefore whoever resists the authority resists the ordinance [diatage] of God, and those who resist will bring judgment on themselves.

The word translated “appointed” in Romans 13:1 is translated from the Greek tasso, which means appoint, arrange, assign, set.  And the word translated “ordinance” in Romans 13:2 is translated from the Greek diatage, which means ordinance, arrangement.  These verses can be understood to say that God is in total control, that all human leaders have their authority and power because God allows them to have it. 

Conclusion

God, at times, selects specific men to be kings (national leaders) for His purpose.  This is probably not the case for all kings.  In other words, God intervenes directly in the affairs of men with an unseen hand, as He sees fit.  However, regardless of how they became kings, all of them are in their positions of power because God allows it.