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You will get this error when your twitter account has not been set up correctly in your iPhone settings.
Simply go to Settings > Twitter and
- ensure your login credential are set up correctly.
- ensure that under apps allowed to use your account, Periscope is switched on.
This setup is annoying because it means you have to store your twitter login in your iPhone which puts you at risk if your phone is stolen.
You are forced to choose between using Periscope or not storing your twitter login credentials in your phone (ie the ‘always logged in’ setting which is a security issue).
Sure you could log in with your phone number but then would have no access to your twitter network.