The song, simply called "Zelda", was actually written (and sung) by a man named Joe Pleiman. It was released in 1998 on an album called Rabbit Joint, by the band of the same name. Neither of which had anything to do with System of a Down.
So how'd this modern internet fallacy come to be? Over ten years ago, the song was uploaded to Napster, in the wild days before the service was shut down and went straight. And it was uploaded simply as "SOAD - The Legend of Zelda", or "SOAD - Zelda". Given this was the early 2000's, many people assumed this meant it was performed by System of a Down, particularly given the similarities between Pleiman's vocals and those of System's Serj Tankian.
The track, which is damn catchy, thus snowballed, and from millions of people System of a Down were given credit for a song they had no part in. Poor Joe. At least he can see the funny side of it, writing on his own website that the 1998 album featured "the song 'Zelda' as unintentionally made famous by System of a Down".
To make up for it, you could go to Joe's site and listen to some of his (and his band's) stuff. In 2003, he was in a band called Splinter, which released an album called Hip Tanaka. Which is an awesome thing to do.
If you've somehow never heard the song, check it out below.