Does God write Poetry?

Yes, you are a poem, written by the hand of Almighty God.   The etymology of the word "poem" goes back to the greek "poiema".  

"Poiema" is found in the Greek New Testament book of Ephesians chapter 2 verse 10 which translated to English reads, "For we are God's workmanship (poiema), created in Christ Jesus to do good works, which God prepared in advance for us to do."

Yes, you are God's poem in progress.  It won't be finished until it is presented at His throne in Heaven without any imperfections whatsoever.