Call me is what guys say often when ending a conversation. It's about the same as, talk to you later or see you around. It's usually said casually and you can bet if a guy says this, you don't have his interest sparked. So what do you do, should you call a guy if he asks?
When a guy says call me, usually it means he may find you attractive and if you call he may talk to you, but it's not something a guy says to a girl who he is very very interested in. If a guy is really interested, he won't ask you to call him, he will be calling you. The only exception to this is if you have been dating for a good while and he asks you to call him. If you have just met or started dating though, he is far from hooked on you yet.
A lot of women take this "call me" literally. They latch on and start calling the guy. This makes them the one doing the pursuing. It tells the guy that you are way more invested into him than he is in you. He sees a woman ready to put the girlfriend crown on and often this causes him to stop all contact and run for the hills.
When a guy says call me, what he usually wants from you is not much. He can live with or without your call. If you do call, you will be setting yourself up as a girl on the back burner. That's what guys do with the girls that do the calling for the most part. They don't see them as a challenge and no challenge means you won't be girlfriend material more than likely.
If a guy really wants to get to know you, he will be the one doing the calling, he won't be asking you to call him. When a guy tells you to call, the best thing you can do is don't. Let him wonder why you aren't so into him. This makes you more of a challenge and more attractive in his eyes. Less is more when it comes to calling men.