Can I use the phrase
Es geht um eine Frage.
Ich habe eine Frage.
What are the differences between them and can I use both for the same situation?
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"Es geht um eine Frage," means, "it goes to the question of... " (an abstract concept, e.g, politeness, righteousness, scientific method, etc., in a general, objective sense of the word).
"Ich habe eine Frage, means "I have a question about..." (that is particular to me).
Apart from sharing the word "question," the two expressions are not alike.
In addition to Janka's answer (which is correct and sufficient) I would - just for exploration of the depths and widths of language usage - present one possible context where "Es geht um eine Frage" anyway would work in the sense of "Ich habe eine Frage", i.e. for preparing an interlocutor to listening to a question:
Entschuldigen Sie bitte, dürfte ich mich kurz an Sie wenden? Es geht um eine Frage: Ich möchte gerne wissen, ob...
Of course, out there in the wild you would not often meet a polite and circumstantial address like this. In much more frequent use is the famously rude
Ich hab da mal ne Frage...