Excellent question, but has two drawbacks:
1) Nuclear waste is very heavy therefore a very powerful rocket would be required to launch a small amount (by volume) of nuclear waste into space. Added to this is the danger of a launch failure which could scatter fallout over a huge area if anything went wrong.
2) IIRC there is a non-proliferation treaty to prevent nuclear material being left in space. This is ostensibly to ensure no-one builds an orbiting missile platform, but also applies to dumping waste as well.
Personally, my own feelings are that should we ever develop a safe and cheap means of reaching orbit (ie a space elevator) then the waste should be sent sunward.