My gift card went through the washing machine and the scratch-off code is missing a few digits now ... is there a way that I can still redeem it??

You can try contacting iTunes Support and see if they can help (you will probably need to give them images of the front and back of the card, and possibly its receipt) : http://www.apple.com/support/itunes/contact/ - click on Contact iTunes Store Support on the right-hand side of the page, then iTunes Cards And Codes