Unfortunately I do not think there is a work around. I have done some searching on this forum, among others, and have yet to find a way to verify without using a phone number.
Just to save you some time, I have already tried Google Voice, TextFree, and a few other apps that offer free phone lines. None of them have worked. I tried them both for the Text/SMS verification as well as the phone call verification - No go. After that I tried a method I found on here using Tropo, but that did not work either :banghead:
There were ways to do it in the past, but FB seems to quickly catch on and change their system.
I am not sure how they do it, but there are a number of people on here that I have spoken with that offer services that can either Phone Verify your current account, or offer you other accounts that have already been verified
Sorry I couldnt be of more help, but just thought I would hopefully save you some effort. Best of luck, and if you do find a work around, I would love to hear the details!