Nope. All transactions address to address are recorded. Now some wallets will try to increase difficulty of finding links between address in such that I have 2 btc stored in wallet 1abc. I want to purchase something from a business for 1btc and the address is 1xyz. Now I send both my btc, 1 to 1xyz and 1 to a new generated address that I have access to 1rrr. Now if someone only knew my address 1abc they wouldn't know if 1xyz/1rrr was the business or my new address. So you'd have to start tracking both addresses! Although you might be able to eliminate 1xyz because you can see it receives 1000s of transactions from other addresses. Assuming the business reuses addresses. 1abc would now be empty.
To truly be private but still use btc I believe your best bet would be through a nontransparent blockchain.
Exchange 1 btc to monero.
Send monero from exchange 1 to exchange 2.
Monero to btc on exchange 2.
Although at the end of the day btc wallets are becoming more clever in how they utilize creating multiple addresses and making the transparent trail hard enough for your average "hacker" to follow.