Then you'll need a new motherboard also, because Athlon 64's do not use Socket A.
If you want to use your current (DDR) RAM, you have the option of using socket 754, or 939
Socket 939 you'll have to get second hand, since AMD have stopped production of 939 CPU's (they've moved on to AM2, which uses DDR2)
Socket 754 is still being made I think, but not in high quantities, and the models are only low-mid range. And you won't get a dual core CPU in socket 754.