Wig Wiggle DJ Scratch is a fairly basic, but ultimately very fun app that allows you to choose songs from your library and play them as a digital record. You can scratch the record all you want, though the similarities to a real DJ's booth end there. With many feature limitations, this isn't a perfect DJ simulator, but it is a lot of fun.
Open the app and you see a large record on the screen along with Load and Play buttons. The Load button allows you to search through your song collection to find a tune to play. It will pull from iTunes so be sure you have at least some songs loaded up into your device. From there, you can press the Play button and start scratching the record. The interface is very tactile, but the visual effects go a long way in selling it. The wobble of the record on the screen, the smooth sound of the scratching--it's all there. Other features like muting, song playback speed, playback position, and more are all missing, but the overall effect works quite well.
If you only want a simple scratching app to play with on your iPhone or iPad, WigWiggle DJ Scratch is a good one to try out. The free version lets you play anything as you would in the full, and you'll get hours of enjoyment out of this because it pulls from your own music library.