Yes. There are several ways.
As Keith says, if you have a Qantas gold or other equivalent gold status, then try status match. Turkish airlines would do status match if you can prove that you fly enough and it’s worth getting your business. Contact them, give them copies of your gold status with other airlines and statement, they should match you.
If you are a nobody and don’t fly enough to ever reach gold, then you can buy Lifemiles gold for ~$2200 USD for 1 year membership. Then you are instant star alliance gold. Personally I don’t think it’s worth it.
If all you are after is lounge access and don’t really care about priority boarding, then you can save yourself $1500 by joining United Club or Mapleleaf club. It’s basically UA and AC’s equivalent of Qantas club, except that you have access to all star alliance lounge whenever you fly star alliance carriers.