Does the Bible Say that God Ever Tempts Anyone?

Why does the Bible say that "God tempts no one" in the book of James, but it also says that God tempted Abraham in the book of Genesis?

Let's examine both texts to which you refer:

Let no one say when he is tempted, "I am tempted by God;" for God cannot be tempted by evil, nor does He Himself tempt anyone.
(James 1:13)

Now it came to pass after these things that God tested Abraham, and said to him, "Abraham!" And he said, "Here I am." Then He said, "Take now your son, your only son Isaac, whom you love, and go to the land of Moriah, and offer him there as a burnt offering on one of the mountains of which I shall tell you.
(Gen. 22:1-2)

In James 1:13, James is referring to hard or difficult times. God doesn't bring destruction into our lives to test us. He is not the one who is causing those things; the devil is.

God put Abraham to the test in Genesis by asking him to do something, or to give something to God. This was a test of obedience, not a trial that God brought into Abraham's life. Notice what happened when God saw that Abraham was willing to obey:

And said: "By Myself I have sworn, says the LORD, because you have done this thing, and have not with held your son, your only son; in blessing I will bless you, and in multiplying I will multiply your descendants as the stars of the heaven and as the sand which is on the seashore; and your descendants shall possess the gate of their enemies.

In your seed all the nations of the earth shall be blessed, because you have obeyed My voice.
(Gen. 22:16-18)