Sure can:

Job 23:8-10 Behold, I go forward, but he is not there; and backward, but I cannot perceive him: On the left hand, where he doth work, but I cannot behold him: he hideth himself on the right hand, that I cannot see him: But he knoweth the way that I take: when he hath tried me, I shall come forth as gold.

Psalms 66:10 For thou, O God, hast proved us: thou hast tried us, as silver is tried. (Proved here means "to test.")

Genesis 22:1 And it came to pass after these things, that God did tempt Abraham, and said unto him, Abraham: and he said, Behold, here I am.

Hebrews 11:17 By faith Abraham, when he was tried, offered up Isaac: and he that had received the promises offered up his only begotten son,

Revelation 3:10 Because thou hast kept the word of my patience, I also will keep thee from the hour of temptation, which shall come upon all the world, to try them that dwell upon the earth. (This is God testing/tempting the whole world during the Tribulation, to see whether they will follow Christ or the Antichrist.)

I am sure there are more verses, but this are the ones that I could find quickly. Based on their contexts, I know they are referring to God testing or tempting us (but not with evil, as James states). There are many other verses about God trying or proving us - which carries some of the same idea, but it also includes the idea of seeing what is already in us (so you could argue whether those are referring to God putting us through a test, or merely examining us thoroughly).