Are you sure you can't do it in lieu of the password? I kept typing my password everywhere until I noticed that you have the choice to either type it in or use your finger (this applies also to every time you're prompted for a password, for example, to install something) - it doesn't explicitly tell you unless you look over at the Touch ID area.
Make sure you have it checked off in System Prefs / Touch ID that you want to be able to unlock the Mac with Touch ID.