Is there a way to stream You-Tube music into a digital amp?

Airplay from your phone or tablet. If your amp is not Airplay ready, get one of those airplay devices with digital out on Amazon for $50.

Thank you

grab an Apple tv box and DL the YouTube app and stream away. can output HDMI and if you find an older 4k unit it also has optical out. 

I've used one for years to stream YouTube, tidal and every other streaming service available on apple devices. It outputs Red book CD quality primarily. Not for critical listening, maybe, but very close and way easier to use then almost any other streamer out there, granted you have a TV in the room. 

freediver

For all the whining your going to get about the poor quality of uTubes lossy format,there is just too much awesome music there you can’t find on the mainstream services to pass them up ...

I’m not sure it’s "whining" to point out that YouTube uses lossy compressed audio, and it sounds like it. Yet there are things on YT that are worth listening to so it’s worth getting the best out of it, imo.

The best solution I found is to access YT via Roku, which I have connected to an HDMI switch that provides a separate digital audio out. That goes in to my Bryston BDA3 DAC. It can sound ok, but I’d never mistake it for real high fidelity.

Yea I agree..For all the whining your going to get about the poor quality of uTubes lossy format,there is just too much awesome music there you can't find on the mainstream services to pass them up,ESPECIALLY music VIDEOs...
An easy way to enjoy them through any system is a USB DAC..There are some pretty good ones from Topping,SMSL & even Audioquest that won't break the $$$...

Doesn’t YT have a commercial streaming service?