Actually scratch that, yes you can!
Many sites are showing it, crunchyroll and hulu are showing it, but theres one free site in particular that has the first 3 eps already, I'll find the link in a bit.
Edit: found a site that is showing all of them (new eps every Thursday at 1 I think...) http://www.daisuki.net/anime/detail/Persona4theGoldenANIMATION