the question is : que estudias?

I am to respond that I am a history major. Am I correct to say Estudio historia

yes or yo se historia

Do not forget punctuation in the question.

¿Qué estudias?
Estudio historia.

Yes, you are correct to say "Estudio historia" to respond that you are a history major. "Estudio" is the first-person singular form of the verb "estudiar," which means "to study." And "historia" means "history." So, when someone asks you "¿Qué estudias?" (What do you study?), you can respond with "Estudio historia" (I study history).