Ranking up

[Kamikaze28]

To answer your question short and concise: there is no fixed amount of games you need to win in order to be promoted.

Now to more detail: when you say 'rank', my first idea is your division rank, which is determined by your points. Ranking up or down depends on the number of games you play, the opponents you face and of course the activity of others in your division.
What I suspect however, is that you're talking about leagues in which case my answer can only be vague. Your league placement and promotion or demotion is based on a hidden matchmaking rating, which is a relative representation of your skill. Over time, this rating rises or falls depending on how well you do. This rating in comparison with the ratings of all other ranked players is used to determine your league and eventual changes of leagues.