After several attempts I somehow managed to get it working. Inspired by this post I basically created the Twitter app again from scratch (see instructions here)
On Twitter’s app settings page I clicked the link in “Allow this application to be used to Sign in with Twitter” and copied the API credentials listed there to WordTwit settings.
All over sudden the “Add Account” link in WordTwit redirected me to the Twitter OAuth page where I had to log in and grant access ??
Not that I know exactly why that finally happened…
Using WP 3.9.1 and WordTwit 3.6 btw