No, I don't think it has. However, it is convenient in a way, since you don't have to change it every year as you turn older, or even remember how old you are :-) . Lots of people find it unnatural, though, and you will never be wrong with "jag är X år gammal".
It's been gaining acceptance rapidly, and it's not uncommon by now. You'll find it in everyday speech, in newspapers, in legal text, in academia, and so on. But calling it common might be a stretch, and there are also lots of people who do not use it.