You don't able to register an AliExpress account via TOR browser. To register it you need enable cookies and JS. These actions deprive your anonymity.
If you want to use AliExpress anonymously you have to do it via special Virtual PC and VPN (or TOR).
A step by step guide:
1. Create Virtual PC using VMvare or any other software.
2. Connect it to VPN or TOR network.
3. Delete the default gateway in TCP/IP settings.
4. Add route to any Internet address via VPN or TOR.
If you do this, you will be able to anonymously use any web browser with enabled cookies and JS.