20:10 Oct 3, 2011 

It is very interesting to look at examples of this expression on the Internet. It seems to be used in various contexts. It can be said by:

A woman looking for a man who will appreciate her femininity and fulfil her emotionally and/or sexually.

A young woman wanting a man who will make her feel grown up (usually, again, sexually).

There are also some lesbian examples (a woman looking for a woman "que me haga mujer"), and many male gay ones: a man looking for a man "que me haga mujer".

It is not always used with sexual connotations, but it often is. It seems to me that in some contexts "make a woman of me" would be more suitable, and in others, "make me feel like a woman".