Not unless you upgrade to Snow Leopard. You must have an Intel iMac to upgrade.
Upgrading to Snow Leopard
You can purchase Snow Leopard through the Apple Store: Mac OS X 10.6 Snow Leopard - Apple Store (U.S.). The price is $19.99 plus tax. You will be sent physical media by mail after placing your order.
After you install Snow Leopard you will have to download and install the Mac OS X 10.6.8 Update Combo v1.1 to update Snow Leopard to 10.6.8 and give you access to the App Store. Access to the App Store enables you to download Mavericks if your computer meets the requirements.
Snow Leopard General Requirements
1. Mac computer with an Intel processor
2. 1GB of memory
3. 5GB of available disk space
4. DVD drive for installation
5. Some features require a compatible Internet service provider;
fees may apply.
6. Some features require Apple’s iCloud services; fees and