THE is correct, although I understand your confusion. You were probably taught that "the" refers to one particular thing, but here it seems to refer to all the pianos in the world. Think about it carefully, though.
If you say "I want a cat," what you are saying is that you want ONE cat, but you're not saying which one in particular. (Remember: "a" is the SINGULAR indefinite article.) So if you say "I can play a piano," you are saying that you can play ONE piano, but you're not saying which one in particular. Of course, that doesn't make sense: You can play any piano in the world, not just one. To say that you can play any piano in the world, you use "the." (My dictionary says that "the" "can be also be used before a singular noun to indicate that the noun is generic.")
A couple of other examples, in case you need them:
* The elephant is the largest land animal. (= Elephants, as a group, are the largest land animals.)
* I enjoy the opera. (= I enjoy going to and listening to operas in general.)