Upvote:2
Scripture says that He can, though I don't think it shows a specific time when he actually does:
Psalm 59:3,8 ESV For behold, they lie in wait for my life; fierce men stir up strife against me ... But you, O Lord, laugh at them; you hold all the nations in derision.
Proverbs 1:24-29 ESV Because I have called and you refused to listen, have stretched out my hand and no one has heeded, because you have ignored all my counsel and would have none of my reproof, I also will laugh at your calamity; I will mock when terror strikes you, when terror strikes you like a storm and your calamity comes like a whirlwind, when distress and anguish come upon you. Then they will call upon me, but I will not answer; they will seek me diligently but will not find me. Because they hated knowledge and did not choose the fear of the Lord,
These two passages ↑ show God doing a derisive laugh which probably isn't what you're looking for.
However this passage ↓ gives great insight on the heart of God.
Ecclesiastes 3:1-8 ESV For everything there is a season, and a time for every matter under heaven: a time to be born, and a time to die; a time to plant, and a time to pluck up what is planted; a time to kill, and a time to heal; a time to break down, and a time to build up; a time to weep, and a time to laugh; a time to mourn, and a time to dance;a time to cast away stones, and a time to gather stones together; a time to embrace, and a time to refrain from embracing; a time to seek, and a time to lose; a time to keep, and a time to cast away; a time to tear, and a time to sew; a time to keep silence, and a time to speak; a time to love, and a time to hate; a time for war, and a time for peace.
God is shown to have done all things in this list (kill, heal, break down, build up, mourn, dance, etc...), so it stands to reason that he also laughs.