Keeping file date

When Copy a file to remote, the file appears with the current date.
It is possible to keep the file original date?

That's what WinSCP does by default. Make sure you have not turned off the "Preserve timestamp" option:
https://winscp.net/eng/docs/ui_transfer_custom
And of course, the server must support preserving the timestamp.
If you need further help, please post a session log file.