Sign in with apple feature on ios 13
Apple's Developer Documentation addresses this question.  In their Human Interface Guidelines for Sign In with Apple they it states:


  To help people set up an account and sign in, it's best to use the familiar buttons that Apple provides for Sign In with Apple. When you use the system-provided API to create a Sign In with Apple button, you get:
  
  
  A button that's guaranteed to use an Apple-approved title, font, color, and style
  Assurance that the button's contents maintain ideal proportions as you change its style
  Automatic translation of the button's title into the language that's set for the device
  Support for configuring the button's corner radius to match the style of your UI
  


There's several examples of buttons designs to fit the look of your app.  You have to use Xcode 11, of course, to get access to this API.

Here's a short tutorial that indicates how to add this feature to your own app.