Is it possible to become androgynous if not born one? and if so how?

Yes learn how: Androgynous means having both male and female characteristics or qualities. Being neither distinguishably masculine or feminine, as in dress, appearance, or behavior. Cultivate the clothes, fashion haircuts, makeup or lack of makeup of the opposite sex and you will appear androgynous. Great example David Bowie sometimes appeared as a beautiful woman. Study androgynous models.

Social learning: Only half of us have attributes that fit gender role expectations clearly. Instead of being just "masculine" or "feminine," or instrumental vs expressive, a sizable minority of people, close to 40% are both assertive AND warm, sensitive AND self-reliant. Androgynous people simply possess both sets of competencies that are stereotypically regarded as masculine or feminine.