Dropbox user authorization without invoking a web browser for login
By design, the Dropbox API doesn't allow this. (We don't want third-party apps to ever handle user credentials.)
Note, though, that the user only has to do this authorization once. From then on, your app can continue to use the access token you got in the first place. The normal flow for a command-line app is to send the user to the browser to authorize and then copy/paste an access code into the console. The app then gets the access token and saves it for future use.