My iMac is running OS X 10.5.8 and when I've tried to install Face Time the installer says I can't because I don't have Security Update 2010-005 although I have successfully installed this and later security updates.
If your iMac has an Intel processor, you can purchase Mac OS 10.6 Snow Leopard. Click on the "Store" tab above or visit any place that sells Mac software. Facetime only works with 10.6.
If your iMac is a G5 or G4, you cannot install Snow Leopard, and you're out of luck on Facetime.