http://forum.square-enix.com/ffxiv/threads/53191-Final-Fantasy-XIV-A-Realm-Reborn-Alpha-test-now-accepting-applications

Go go go! :D

ETA: If, for some bizarre reason, SE takes down that thread or something, here are the relevant links:

Japanese Alpha Test Site Registration : http://entry.ffxiv.com/alpha/index.html
North America Alpha Test Site Registration : http://entry.ffxiv.com/alpha/index_na.html
European Alpha Test Site Registration : http://entry.ffxiv.com/alpha/index_en.html