Yes, you can use the public key authentication. But for that you still have to store the private key along with your script. Normally the key is encrypted with a passphrase. To automate the login, you would have to store the passphrase to the script file anyway (using the -passphrase
switch). So still, if anyone gets an access to your machine, he/she is still able to steal your identity, just as with the password. Though there's an advantage. You can have multiple keys (while only one password). If you use a special key for the script and the key is ever compromised, you can revoke it, while keeping the other keys.
Note that, if you are not absolutely sure of the physical and electronic security of the system on which you are connecting, there's hardly any way to setup an automatic authentication. If you are sure about the security, storing password in the script file is just ok.
Anyway, your question is mostly duplicate of:
How do I setup Public-Key Authentication?
For WinSCP specifics, see the guide to Setting up SSH public key authentication.
See also the WinSCP guide to Protecting credentials used for automation.