Yes, in v3 of the site or via the apps. That said, not very many people know about its availability so getting a game is likely to be hard. Unless you know someone is on the same time as you are, in v3 or the app also, and you directly challenge them.
How to play live in Chess 960
Maybe it will be possible to actually get games once V.3 is the default, but even then the option to play variants is kind of buried. Just go over to lichesss.org when you want live 960.

Hello, could anyone explain where the option is? I tried "Try the new Chess.com" and went to Live, but no 960 button as far as I can see.

In Live, click the button that looks like a chessboard, next to the time control and "Play" buttons. That's where you select the variants.

Yes, in v3 of the site or via the apps. That said, not very many people know about its availability so getting a game is likely to be hard. Unless you know someone is on the same time as you are, in v3 or the app also, and you directly challenge them.
The best way is still to go to lichess.org, where you can easily play 960, crazyhouse and many other variants live. Its sad that chess.com took so long to come with something which is so much less inviting than lichess already had. Chess.com is still better for a lot of stuff - just not variants.
Does Chess.com can play live in chess 960 ?