I looked up what numbers I could find, according to the OECD's Road Safety Annual Report 2016, in 2014 the US averaged about one death per 150 million vehicle-kilometers (vkm) (6.7 killed per billion vkm).
According to Waymo's own page on the subject, they have driven "more than 5 million miles" (8mvkm) since 2009[0] and they seem to be by far the lead vkm producer in the autonomous space[1]. Just to be as safe as 2014 US human driving they need to clock in an other 140mvkm with no more than one fatality, and even then that could be debated to be in more selected conditions than human driving.
Don't get me wrong, I'm a big believer in autonomous driving and I think it would be a great, great thing, but saying it is already safer than human driving is at best misleading.
[0] https://waymo.com/ontheroad/
[1] https://www.theverge.com/2018/1/31/16956902/california-dmv-s...