Your question is ambiguous, sorry.
'Fire arrow' is a compound noun, meaning an arrow that has flames, and I have not heard that used. The closest would be a 'flaming arrow'.
I guess you are asking if you would say 'fire an arrow', i.e. did we use the verb 'fire' with the noun arrow?
It is certainly the correct verb now, but it is an interesting question to ask if it was correct historically. On TV programs, they often use the verb 'loose' with arrows. I don't know if that is historically correct, and whether that was the standard word back then, sorry.