There are several websites already online that feature ask a rabbi feature (Ask Moses, Chabad, Aish's Ask The Rabbi, Beit-El Yeshiva Center, and even Reform Judaism are just some sites that have this feature).
The step beyond this is for SMS ask-the-rabbi, which Rabbi Shlomo Aviner has taken up, with his ongoing Shut SMS series (#1, #2, #3, #4, #5, #6, #7, #8, #9, #10a, #10b, #11a, #11b, #12), about which Rabbi Adam Mintz discussed a similar thing of Rav Aviner's couple of years ago (although not SMS Shut, per se) in his teshuvot series of lectures.
Over this past weekend, Dani Klein and I were talking about the opening there is on Twitter for an ask the rabbi account (he actually mentioned this online on Wednesday) and although I'm not sure I would be up for such an idea, myself, I do think it's a good idea. In fact, I'm surprised Chabad is not already on to this yet (although there is @ChabadOrgNews and @Lubavitch, but they are not doing question and answers). Anyways, this is an as of yet unexplored niche and it will be interesting to see what will become of it.