You can use the "Mass Subscribe" function to upload a current subscriber list or paste in a lot of email addresses to subscribe to a mailing list.
From your cPanel interface, go to Mail -> "Mailing Lists". Find the list you want, click "Modify", and log into the mailing list administration interface. Go to "Membership Management" -> "Mass Subscription".
Here you can paste a list of email addresses (one per line) or upload a file containing the email addresses (one per line).