Can I put a rack on a carbon road bike?
It is (strongly) not advisable to put a rack on carbon.  

You could probably put a lock mount on the handlebar stem (I do).  

You could get an over-sized seat bag.   

Possibly a handlebar bag.  

Bottle cage bag but they don't have much capacity.  They are good for like wallet, cell phone, and keys.

Don't like to do product recommendations but Revelatedesigns have a lot of bags.

Not easy to find but there are carbon forks with rack eyelets. But I would not do that to that bike.

Not a typical commuter bike.