Is there a free demo for Rome: Total War on the Mac?
Check on the Steam store. I know that the game is on there, and for a lot of their games they have trials as well as the purchase option. Though you should always use Steam to buy and try games if at all possible, if you don't already.
I did a quick search and all the forums I visited say No, the demo is not available for the Mac.
Maybe one of the others will have better luck.