You can play the FrameWork system, the one used for CthulhuTech using playing cards. My players actually preferred it. If you have access to C-Tech you can massage that system into other genres depending on your group's taste.
WUSHU, of course, does have die rolling but it's minimal and you could easily nominate someone to actually do the rolling, whoever can hold the box you roll the dice into.
FATE probably wouldn't work as well, you need to track FATE points and roll dice frequently, depending on what setting you are playing.