If you can get a copy of Warcraft III installed on another Mac, you should be able to run it just fine under any version of OS X, including Mavericks (10.9). The trick is finding a machine still running a version of OS X old enough to support the Rosetta environment. For this, you will need a Snow Leopard or older version of the OS and an Intel machine. Once you have it installed and updated to the very latest, you should be able to copy the entire Warcraft III directory from that machine to your current machine. You may have to re-enter your CD code, but that should be the easy part.
And yes, this has been tested. I restored my copy of Warcraft III and the Frozen Throne expansion from an old backup to a 2014 retina MacBook Pro running Mavericks 10.9.4 and I was able to launch and get into a local game.
Update: only local games will work under Mavericks and later. This is because WC III uses OpenTransport for it's networking, but Apple has removed OpenTransport support starting with Mavericks. If you only want to play against the AI, this won't be an issue. But for everyone else, this is less than ideal.