No.
Hacking

Is it possible for your opponent to hack into your game and make a move for you?
No. But they can hack into your brain and force you to make a stupid move.

In theory yes, in practice, not likely. (Notice I did not say impossible)
Server errors are far more likely, if you are trying to say someone hacked the servers/ your computer to make a move for you.

Of course it is possible to hack your account. One only needs to log in with your username and then guess the password.
Tough going but possible.

IM Deviate-and Philidor-different opinions-who is right?
If someone can somehow get your login information for a site, through keylogging or directly hacking your computer etc, they can basically do any online operation you can do on that site with your account. So, yes, it's possible to get your chess.com account hacked, broadly speaking. This is probably the case for every online site that asks for a login information.
However, there's nothing an opponent can do while just playing games with you on chess.com, through chess.com. I assumed that's what you meant, so I answered no.

Is it possible for your opponent to hack into your game and make a move for you?
LOL logicon, inventive I'll give you that much. (You know what I mean)
Is it possible for your opponent to hack into your game and make a move for you?