Can I replace my scratched rear case?

Extremely time consuming and difficult.

But, It can be done.

You would need to buy a new rear housing and then completely disassemble your phone and reassemble it to the new rear housing.

I do not believe ifixit sells rear housing for the iPhone 3G. Check eBay.

(There are a lot of fake iphone parts so beware when buying, check the sellers feedback for quality of products.)

Here's the iFixit step-by-step guide to removing/replacing the rear panel (rear housing)

iPhone 3G Rear Panel(Housing)

Best of Luck!

-Varsity