On the rare occasions I've had the testicular fortitude to ask for anything from a woman, I've gone with asking for an email address rather than a phone number. Like the OP, I read "can I have your number?" as "Can I have a long-term license to annoy the crap out of you in future?" Though in my case it's just because I hate talking on the phone.

Asking for an email address seems to fit the social formula while being easily blackholeable at a future date.