Hey @gwenlee ,
At this point in time, you are unable to archive themes. You do have the option to change which theme is live on your online store, make a backup copy of a theme that you want to customize, download a theme for future use, remove an unused theme, and update an older theme to the current version.
May I ask why you want to archive your current theme? If you are wanting your current store to not be accessible to the public but are wishing to still work on it behind the scenes, you are able to enable a storefront password. The password page is a landing page that adds password protection to your online store. You can create a password and give it to customers that you want to enter your store. Only the password page of your store is found by search engines. Other pages, like product pages, are hidden, and search engines won’t display these pages in search results.
You can add password protection to your online store by following the instructions listed in this help guide.
Let me know if I can clarify anything further!