Question: How does God choose leaders without affecting their free will?

Question: Is it correct to say that God doesn’t choose our leaders but that He can raise up and bring down leaders using circumstances, without affecting their free will, in order to carry out His purposes? 

Response: It is certainly true that in Psalm:75:6-7 [6] For promotion cometh neither from the east, nor from the west, nor from the south. [7] But God is the judge: he putteth down one, and setteth up another.
See All... we are told that “Promotion cometh neither from the east, nor from the west, nor from the south. But God is the judge: he putteth down one, and setteth up another.” In the process of “putting down” and “setting up,” He will use circumstances to accomplish His will without stifling the free will of the individual. To say that God “does not choose our leaders” is a point that certainly will be debated, in view of the fact that His use of circumstances reveals His will concerning the leaders who are set up or put down. That choice, however, is not the same as the Calvinist idea of sovereignty would allege.

The Bible teaches (Acts:10:34-35 [34] Then Peter opened his mouth, and said, Of a truth I perceive that God is no respecter of persons: [35] But in every nation he that feareth him, and worketh righteousness, is accepted with him.
See All...) that God elected to save every soul who “fears God and works righteousness.” Before man’s creation, God elected that men would be saved “in Christ” (Eph:1:3-4 [3] Blessed be the God and Father of our Lord Jesus Christ, who hath blessed us with all spiritual blessings in heavenly places in Christ: [4] According as he hath chosen us in him before the foundation of the world, that we should be holy and without blame before him in love:
See All..., 7-12).God gave His plan for the redemption of man (Eph:3:10-11 [10] To the intent that now unto the principalities and powers in heavenly places might be known by the church the manifold wisdom of God, [11] According to the eternal purpose which he purposed in Christ Jesus our Lord:
See All...). He also granted that man would have free will, which is simply the ability to choose to obey or disobey Him (Gn 3:1-6; Josh:24:15And if it seem evil unto you to serve the LORD, choose you this day whom ye will serve; whether the gods which your fathers served that were on the other side of the flood, or the gods of the Amorites, in whose land ye dwell: but as for me and my house, we will serve the LORD.
See All...; Mt 11:28). Again, without at least that measure of “free will,” as Dave Hunt has noted, Joshua:24:15And if it seem evil unto you to serve the LORD, choose you this day whom ye will serve; whether the gods which your fathers served that were on the other side of the flood, or the gods of the Amorites, in whose land ye dwell: but as for me and my house, we will serve the LORD.
See All... becomes meaningless.

So your statement is accurate, although the idea of God “choosing” someone is certainly reflected in His use of circumstances to accomplish His will.