Zcash z-addr in bitcoin Can a improvement, difficult or easy, to Bitcoin Core implement z-addr like Zcash?
Zcash do it possible to send coin anonymous using z-addr. The blockchain do not show z-addr, only t-addr that is like a bitcoin address.
The developers of Zcash did try to implement their solution using the Bitcoin blockchain but it required several changes to Bitcoin core that where both difficult and more importantly difficult to come to consensus for the changes with the rest of the Bitcoin community. So the Zcash developers decided to make a new blockchain.

So technically speaking it would be possible (but hard) but convinving the Bitcoin community of the changes would be much harder.

Note that there are other anonymity proposals that will use the Bitcoin blockchain (e.g. Confidential Transactions, MimbleWimble) but I do not know the state of their implementation.