One excellent way to memorize the scripture is to sing a verse. As I have gotten older and my ability to memorize has decreased, I have found myself depending more and more on this technique. There are some well-known verses that have been set to music or you can make up your own melodies. You can even chant or rap the verse to help you memorize the words.
I have included a recording of the instrumental melody and example recordings of how the song sounds. There is an example of singing the song using the traditional King James Version, which is the way that I first learned this song, and an example of how you can alter the song in a different version. I used the English Standard Version, but you can memorize with any version of the Bible. Just make the words fit the melody.
Instrumental Melody (organ):
Instrumental Melody (music box) :
King James Version: He hath shewed thee, O man, what is good; and what doth the LORD require of thee, but to do justly, and to love mercy, and to walk humbly with thy God?
Example song (KJV):
English Standard Version: He has told you, O man, what is good; and what does the LORD require of you but to do justice, and to love kindness, and to walk humbly with your God?
Example song (ESV):