Literally, "call me". May be said by someone who doesn't want to do the calling themselves, for various reasons.

1) When a person is attracted to another person but does not want to seem too eager, and so makes the other person ring them. Ironically, this request does exactly what they don't want it to do.

2) What teeny-boppers say to Justin Timberlake at a concert whilst throwing a post-it with their phone number to him in the vain and naive hope that they have a chance in hell.

3) This is usually said by a girl. Said girl then sits by phone all day complaining that (s)he hasn't called. Problem is, they didn't specify a time to call.

4) Said at a rushed moment whereby the reasoning behind such a request is not divulged, and usually ends with a frantic handwave from the speaker (and occasionally a dumb grin whilst walking backwards)

5) Used in business/school, not always with words, but with the universal two-fingered phone sign by the ear. Can also be accompanied with miming of "call me" as if that helps when you're on the other side of the room.

girl's way to test how interested the dude is in her.

Phrase used when someone wants you to give them a phone call at a later time.

Let's do it.

to call someone..using some sort of telephone (communication device before instant messaging)

The two words, six letters that represents so much more than a period ever could. It is the dagger that ends confrontations and conflicts. Meaning exactly the opposite of actually "call me".

It is also highly frowned upon if recipient of a "call me" hammer actually calls sender.