Answer:
You might write this as, "La hora es la una de la mañana", or "La hora es la 1:00".
If you were trying to write 1:00 PM as opposed to AM, you would simply change it to "La hora es la una de la tarde", or "La hora es la 13:00"
If this does not work for you, you could say "Es la una de la mañana" or "Es la 1:00)
(Note that you can include en punto, which means "o'clock" or "on the dot" when translated to English. It's not necessary though.)