"my older brother"
While you are correct that 兄 / 兄さん (ani/niisan) is usually used to refer to your own brother and お兄さん (oniisan) as the more polite form is used to refer to someone else's brother, I have seen them both interchanged as well.
For example "oniisan" can be used to refer to your own brother if there is a large distance between you as siblings, it's as if you are saying you don't know him very well or don't want to know him. And in the same way someone could use "niisan" to refer to an older male who is not a relative but who is someone who is important to you.
This usage is probably more common in manga than in daily life though, just want to point it out for those who didn't know.
I hope I got the kanji right, I'm still a newbie!
Only use お兄さん/おにいさん when referring to someone else's older brother, not your own, as it is considered rude. On the same token, always use 兄/あにwhen referring to your own older brother. In Japanese, you should always use humble words towards your own family and honorific terms for another's family.
Because there is no "is" in the question. They're asking for a phrase, not a full sentence. If it asked you to translate *he is my older brother." then you could write 私のあにです