9 years ago we announced an app that did this right here on Hacker News. https://news.ycombinator.com/item?id=2285594
How we did it: We hired the AT&T lady to make a recording that said, "Press 1 for your next caller". We played that on a loop for operators. When we detected a DTMF "1" we'd call your cellphone and connect the calls. We had most of the big companies in the app, but failed in the end because we couldn't find a business model. My first VC-funded startup. :)
Site is still up! (But not longer mine) http:/www.fastcustomer.com/
What I'm up to now: http://www.happymonday.com/ (helping people find work based on mutual values, priorities and functional work culture fit.)