Bible Trainer ESV 1.7.1

Once you've chosen a passage to memorise, the app will break it up into phrases and give them to you one at a time, making it easier to memorise. As you get to grips with the passage, you'll begin to be able to say it without reading the text, but you can still use the app to remind yourself of what comes next. You can also test yourself by typing the passage out; the app will correct you if you make a mistake. The app stores all the passages you're working on, helping you to keep track of what you've done. Similarly, the app can store prayer requests, and you can set reminders to pray for people or recap a Bible passage.

If you're like me, you'll need some pretty strong motivation to want to memorise scripture. How about this:

John 15:1-11 I am the true vine, and my Father is the vinedresser. (2) Every branch in me that does not bear fruit he takes away, and every branch that does bear fruit he prunes, that it may bear more fruit. (3) ALREADY YOU ARE CLEAN BECAUSE OF THE WORD that I have spoken to you. (4) Abide in me, and I in you. As the branch cannot bear fruit by itself, unless it abides in the vine, neither can you, unless you abide in me. (5) I am the vine; you are the branches. Whoever abides in me and I in him, he it is that bears much fruit, for apart from me you can do nothing. (6) If anyone does not abide in me he is thrown away like a branch and withers; and the branches are gathered, thrown into the fire, and burned. (7) IF YOU ABIDE IN ME, AND MY WORDS ABIDE IN YOU, ask whatever you wish, and it will be done for you. (8) By this my Father is glorified, that you bear much fruit and so prove to be my disciples. (9) As the Father has loved me, so have I loved you. Abide in my love. (10) IF YOU KEEP MY COMMANDMENTS, YOU WILL ABIDE IN MY LOVE, just as I have kept my Father's commandments and abide in his love. (11) THESE THINGS I HAVE SPOKEN TO YOU, THAT MY JOY MAY BE IN YOU, AND THAT YOUR JOY MAY BE FULL.

What's the outcome when we abide in Jesus and his words abide in us? Being clean (verse 3), fruitfulness (verses 4 and 5), salvation (verse 6), communion with God (verse 7), abiding in Jesus' love (verse 10) and fullness of joy (verse 11)! And what better way is there for Jesus' words to abide in us than for us to memorise them?

If you still need convincing, I doubt I can say it better than John Piper:
www.desiringgod.org/blog/posts/ten-reasons-to-memorize-big-chunks-of-the-bible