You sure can, with our iOS app (as long as your Apple device is Touch ID-enabled).
When you sign up for an account through our mobile app, we'll ask if you want to use Touch ID to log in to your MogoAccount. You can choose to set it up then, or skip it and enter your password to log in.
If you change your mind, you can also change your Touch ID settings in your Account Settings.
If your device is Touch ID-enabled but you don't know how to turn it on, visit this page.