If you created a custom template in Word, you can use it in Word for the web after you save it as a document (.docx file) in OneDrive.
To create a document from a template, create a new document from the template in Word and save the document to OneDrive. Then save the document in your OneDrive following these steps in Word.
To use that document as a template, open it in Editing view in Word for the web and select Create a Copy. You can choose to Create a copy online or Download a copy. Use the copy as the starting point for your new document.
Try it today in Word for the web.