Some guys, when they meet a girl, instead of asking her for her phone number, they actually give the girl their business card, telling her "Call me sometime" or something like that. This is not a good idea for at least to major reasons:

First, many girls will consider it tacky, especially the ones who have been around, who have been meeting guys and dating and who figured out what they like and what turns them off. They know, like you should, that there is no places for business cards in an interaction which is very personal, such as meeting someone for the first time and trying to establish some kind of romantic connections. 

Secondly, it's generally not a good idea to give out your number and you should always try to get the girl's number instead, because mother girls, even if they are interested in a guy, will not want to be the one calling first. They know it's the guy's job and they want to know that he is the one who makes the first move. So ask for her number instead of giving yours. Besides, it's much more fun calling when you decided to, than wonder when and if the girl you met is going to call you.