On face value, there is a contradiction between James 1:13 and Psalm 106:14, at least in the King James Version.
James 1:13 says
Let no one say when he is tempted, “I am being tempted by God,” for God cannot be tempted with evil, and he himself tempts no one.
Yet we are told in Psalm 106:14 that Israel had “tempted God in the desert” (KJV). Modern versions translate this as God being “tested” rather than “tempted”.
This is a translation problem. These days, the English word “tempt” suggests a desire to sin. It used to also mean “test” (the OED lists this as an obsolete meaning of “tempt”). So the KJV was a reasonable translation for these verses when it was produced in 1611, but it is now misleading. The Hebrew word translated “tempt” or “test” is נסה (nasah) which means “to test, to tempt, to prove” (NET Bible notes). Thus, the Hebrew word is broader than our words test or tempt.
The Septuagint (an ancient Greek translation of the Old Testament) translates the word nasah in Psalm 106:14 as ἐπείρασαν which is related to the Greek word that James uses. So James is teaching that when the word is applied to God, it cannot carry the meaning of “tempt him to sin”, but only of “test his patience”. This is consistent with the rest of Bible teaching that God is unable to sin.