After each Uber ride the driver and customers are able to rate each other if they so choose to do.
You have been able to get your Uber rating in the past by sending an email to customer service but this is no longer necessary. You can use the following steps to get it from the app.
And I’d like to know my rating
Just did a search to my email and seems that I have used Uber roughly 400 times since I signed up for the service back in 2014. I use the service pretty much anywhere it is allowed and taxis only in cities/countries where Uber is not available (like here in Malta).
My default driver rating is five. If the driver is annoying or issues with the car/service, I start dropping the stars.
I guess that you could theoretically use this to see what rating the driver gave you. If the average went down, he/she must have rated you less than five.