Never used Anki myself but after finding the web site and read the instruction manual I found the instruction "Running from a Flash drive". If you look under the heading Managing Files and your Collection it should give you more information. Hopefully the instructions below will help.
Anki can be installed on a USB / flash drive and run as a portable application:
Copy the \Program Files\Anki folder to the flash drive, so you have a folder like G:\Anki.
Create a text file called G:\anki.bat with the following text: anki\anki.exe -b \ankidata
If you would like to prevent the black command prompt window from remaining open, you can instead use: start /b anki\anki.exe -b \ankidata
Double-clicking on anki.bat should start Anki with the user data stored in G:\ankidata
The instructions above may not be clear. When it says Create a text file called G:\anki.bat what it means is to save the file to your USB as anki.bat (.bat being the file extension instead of .text)