You're not trying to create a duplicate Angry Birds game, so it's unlikely you'd run afoul of their patents or copyrights (but see the end of this answer). The operation of your app is totally unrelated to the functionality or appearance of the Angry Birds game; you would simply like your app to be used by people who are also users of Angry Birds.
I imagine the primary difficulty impediment here would be trademark law. You are forbidden from causing consumer confusion over the source of your app. If you use the trade name "Angry Birds" in a way that would lead users to believe that your app is produced or endorsed by the owner of the trademark "Angry Birds" then you're in some legal hot water. Since you want to say, "This is an app for people who play Angry Birds," but at the same time constantly clarify, "This app is not associated with the creators of Angry Birds," this might be a difficult line to walk.
Even if you fall over yourself clarifying at every turn that your app is not endorsed by the creators of Angry Birds, they may still sue you, purely because trademark owners can lose their trademark if they fail to defend it effectively from misuse. This is because trademark is primarily intended to protect consumers. A trademark owner who fails to guard consumers against confusion may lose their right to their mark, since they have failed to use their mark for its intended purpose.
Perhaps I'm being overly paranoid, though -- surely this has been done before. Virtually any popular app is bound to have fan sites. You might look to see how popular fan sites and discussion boards for major games disassociate themselves from the makers of the game they discuss. If you want a professional assessment of how best to do this, of course, consult a lawyer.
Finally, you might also run afoul of copyright if you include art assets from the game in your own app. Don't do this, unless you get permission beforehand or are prepared to defend yourself in court.