It was the grace of God that chose Abram to become the Father of a Nation that would produce a descendent, the Messiah, through whom all nations would be blessed.
Nehemiah 9 makes it very clear that God chose Abram; Paul writes in Ephesians 1.4 that God chose us in Him before the foundation of the world.
God chose Abram and God chose you if you are born-again because there wasn't any work that Abram, I, or you could produce that would make us worthy of being called—thus even our calling from God is a work of Grace.
Paul says for by grace are you saved—not of works lest any man boast—therefore, even my faith or belief or act of believing cannot be a work which I do. Although it very well may seem to me that I believe—I know I am—yet the Bible prevents me from making faith or belief a work.
Maybe Paul instruction in Gal 2:20 would be helpful right about now as we wrestle with am I believing or is my belief in Christ as my savior as gift?
I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me.
The answer is yes and yes.
It is a gift and an act of the will—both. According to the Bible, God found Abram's heart faithful after He chose him and after He called Him from Ur, not before. Perhaps we are unwilling to acknowledge the degree upon which we are dependent upon God for even our faith to believe. Somehow we must, in the deep recesses of our mind, believe that we did something to contribute to our salvation.
By some means, we have been convinced that God cannot command us to do something that is impossible for us to do alone—yet, the presentation of the Sinai Covenant was designed for the express purpose of showing mankind how much he needs the grace of God to be able to live in obedience to the commandments of God—even the commandment to BELIEVE.
Joshua 24 presents Abram as an idolater before the call of God in his life—therefore; we may rightly conclude that God did not choose Abram because Abram chose God. Yet the Bible says "Abraham believed God." So, I do believe. Yet not I, but by the Spirit of Christ that lives in me am I able to believe.
A totally depraved man—dead in his trespasses—does not have any ability in and of himself to believe outside the grace of God. He needs to be "quickened" or made alive (Eph 2). Yet this quickening is invisible and transparent to me—therefore, I think I believe because it appears to me that I believed and he saved my soul—which I did. But the Bible requires me to understand the depth of my salvation afterwards—child like faith saves a soul.
But every disciple of God is commanded to: "Grow in grace, and in the knowledge of our Lord and Savior Jesus Christ. To him be glory both now and forever. Amen (2 Peter 3.18).
Thus the Grace of God is supremely magnified in God's call of Abram and that same grace is what saves men even today.