In the online version of outlook, you can still create and use a signature, following these steps will allow you to do so. First you will need to fine this icon:
Click on it and scroll to the bottom of the menu that appears until you find the the "View All Outlook Settings" link, click on the link.
On the new window that appears, choose "Mail" and then "Compose and reply"
On the Compose and Reply page you will see the signature box below, enter your signature in this box. You can set this to be used when creating a new email and forwarding an existing one from your mailbox.