Yes, but it's a complex process (overly complex) like most of what happens with Australian firearms laws, and also costs more than it needs to (again, common with Australian firearms laws).
You would have to put the weapon into the hands of somebody who is permitted to have unregistered firearms in their possession (generally a gun dealer who would charge you for this). Then you would have to get a 'Permit to Acquire' (which costs you money) for the weapon. Assuming it's a weapon you're licenced to have, it after the PTA is processed, it can be transferred back to you as a registered firearm.
At least that's how it works in my state (Victoria).
Sounds like a whole lot of trouble. I think I remember something about having to have your guns secured in your house at all times too. Does someone from the government show up at your house to check on that as well?