Like Wii is, Wii U is capable to play Nintendo GameCube games, and because of that, it is also capable to play GameCube games backup thanks to diosmios.
DiosMios make possible to play GameCube backup from USB devices or directly from a SD card.
To install it:
Download the latest version of DiosMios on the official download page, with a wad manager.
Copy your game on the directory Games on a FAT32 partition #1 of a HDD (slot 0 on Wii) or a SD.
Run it thanks to a compatible loader (ie. USB Loader GX)