TaxiMagic does exactly that. Apps for Android and iPhone, free to use if you pay cash, a fee to pay with CC thru the app. I use it for short trips in SF and Ube

TaxiMagic does exactly that. Apps for Android and iPhone, free to use if you pay cash, a fee to pay with CC thru the app. I use it for short trips in SF and Uber for longer trips. It always takes less time for the Ubermobile to show up than a taxi.