Is it weird if a woman approach a man for a potential relationship (like woman picking up a man)?

Culturally bound: No, not weird in the general, American culture - current trends are moving to more egalitarian roles in dating. However the overall answer depends on one's cultural beliefs and expectations, as well as the cultural norms which one is operating/living in.

Relationship Needs: It is natural to have desire for a relationship Have relationship in which you can have heart to heart talk, feeling comfortable to express your opinions, feelings, interests It is ok to take initiative to reach out to a man to have beginning of relationship. Respect yourself and do not be desperate to have a quick relationship. See a Therapist to understand your needs, feelings and behavior.