I'm using AMAZON ec2's server now. I'm in the US east zone so my users from Asia found that my site is extremely slow.
How can I handle this? Can I set up a multiple zones server at EC2?
Sure, EC2 also has a region in Singapore. You can also use the Amazon Route53 latency based routing to direct your users to your nearest server - users from Asia will then use the Singapore server.
However your application will have to deal with code deployment, keeping in sync, using the same database or syncing different ones etc. As this depends mainly on the type of your application, there is no general rule about how to handle this. I would suggest to think about this first before setting up a server.