Uber has 160,000 active drivers in the US

"Ride-hailing company Uber announced plans Tuesday to create 1 million jobs for women as drivers in the next five years — offering a rare peek into its growth plans.
In the U.S., where Uber got its start six years ago, the company boasts 160,000 active drivers. Fourteen percent of them are women.
Globally, the number of drivers is less clear, but Uber boasts "hundreds of thousands" of driver partners around the world, Uber spokeswoman Kristin Carvell told USA TODAY.
Even if one conservatively assumes that Uber has as many as 900,000 drivers in the 55 countries where it operates, and that 50% of those drivers could be women in 2020 — Tuesday's announcement suggests that Uber expects to at least double its growth over the next five years."

Source:  USA Today, 10th March 2015