nope, sorry. gamecube games aren't compatible with the Wii U. Hovever, it is a rumor that Gamecube games will come to the Wii U in some kind of virtual console. however, it's just a rumor currently.
Wanna add this: Reggie has said that he "would love to see Gamecube games on Wii U VC." So I'd say it's a possibility.
In addition to what Earthbound stated, there's a reason they aren't compatible. It's because they removed the GCN controller slot, and memory card slot.