This video is not new. But damn, it's cute.
Here, we have a cockatiel singing the theme song for the Studio Ghibli film My Neighbour Totoro. This video is from YouTube user asayasufuraion, and other YouTube users have also uploaded videos with birds singing anime songs.
For example, here's the Ponyo theme from puchipiyo:
And now I have these songs stuck in my head. Thanks for that, birds!