How implement fingerprint scanner in WebApp?

It is now possible to use fingerprint authentication but also other strong authentication methods on Chrome.

The Web Authentication API is introduced and explained in the article below which also contains a video from the Google I/O'18 session that presents and demos its features.

https://developers.google.com/web/updates/2018/05/webauthn

Try the API yourself at https://webauthndemo.appspot.com/

If you want the access to the fingerprint itself, then no, you can't.

If you just want to delegate authentication to the underlying device without caring much how it actually happens, there is a standard for this: Web Authentication API. The problem with this API (like with other young APIs) is that it is not yet well supported. In Chrome the status is "in development". Edge seems to support it with Microsoft Passport.

But generally, if you're looking for a decent, mature solution, you're out of luck.

It is now possible to use the Web Authentication API in all major browsers, including iOS.

This is a very important development for PWAs.