Singing as such is an art, it's planetary ruler is Venus and if you want a house, for horary it would be fifth.
However, things are never quite that simple. Usually there is a reason for singing - if it's to entertain others then it's still fifth house, if it's a hobby it's fifth house, if it's something you do in the bath, then it's fourth house (assuming that your bath is in your home) If you are interested in it as a career, you'd be looking at the tenth house, and hoping that either Taurus or Libra was on the MC (it's a Venus career!) or that Venus has a good dignity in the sign of the MC, such as Exaltation, or Triplcity rulership (obviously Venus is ruler in Taurus and Libra). If you're standing on the street busking, then it's tenth house (your actions) and what you get in the hat is second house.
If you take on a singing coach then he or she is ninth house (the expert) but again you'd want Venus in some dignity. If the purpose of singing is to communicate a specific message then it's third house, the process of composing, clearly has some third house connotations.
The key therefore becomes what is the question and what particularly is the role of singing in the question.