You have said it very clearly and naturally already! "I have time every Tuesday at this time." You could say it several different ways as well, e.g., "I am available every Tuesday at this time" or "Every Tuesday at this time is good" or "Tuesdays at this time works for me" or "I have time every Tuesday at X o'clock".

You could also say 'I am free at this time every Tuesday.' It isn't very formal, but would definitely work in this context :)