As @SavGuard already answered, you can actually use WinSCP as a better session manager for PuTTY.
There's no additional work comparing to opening the session in PuTTY directly. You can open PuTTY straight from WinSCP Login dialog. You do not have to open the session in WinSCP first.
But to answer your literal question: WinSCP uses a very similar storage format for saving the sites as PuTTY does.
So if you export the WinSCP registry key:
[HKEY_CURRENT_USER\Software\Martin Prikryl\WinSCP 2\Sessions]
[HKEY_CURRENT_USER\Software\Martin Prikryl\WinSCP 2\Sessions\MySession]
"HostName"="example.com"
"UserName"="username"
And replace HKEY_CURRENT_USER\Software\Martin Prikryl\WinSCP 2\Sessions with HKEY_CURRENT_USER\Software\SimonTatham\PuTTY\Sessions, and import back, it should more or less work (though not all settings will import correctly).
As you currently use an INI file with WinSCP, you will first have to switch to registry storage.