I have followed the instructions in https://developers.google.com/bigquery/authorization#service-accounts-appengine to make some queries from app engine to bigquery.
Actually there are two areas from where you can add an account. If you go with old console code.google.com/api/console it would take you to your appengine.google.com dashboard i.e "Way-1" which actually has some problem of asking "Verification". The new https://cloud.google.com/console has solved this problem.
[Way-1] *Problemtic* hit http://appengine.google.com ==> your_app_name> ==> Permissions
[Way-2] *Works* hit http://cloud.google.com/console ==> Click your_app_name ==> Click Permissions on Left Pane ==> Click Add Member Button and add i.e xxxxxx@appspot.gserviceaccount.com with "Can Edit" rights
"If you already have added your account via Way-1 Follow below method"
"Way-1" seems to have some problem due to this your account will keep showing "Pending Status". If somehow you have added the account via Way-1 and try to follow "Way-2" afterwards you would keep seeing the same status at way-2 link. For it you'll have to delete that user with "delete icon" which appears on mouse hover. Delete the account from there and add xxxxxx@appspot.gserviceaccount.com with "Can Edit" permission.
You can add the xxxxxx@appspot.gserviceaccount.com to the project at http://cloud.google.com/console.
Expect this to be easier/ more straightforward soon!
Step by step, by @Christian: