The Dropbox OAuth app authorization flow supports the "token" and "code" flows. You can find the documentation here:
https://www.dropbox.com/developers/documentation/http/documentation#authorization
A redirect URI is required for the token flow, but not the code flow, so if you need to process the app authorization without a redirect URI, you'll need use the code flow. That will result in an authorization code displayed on the Dropbox web site that the user can copy and paste into your app to complete the process.