You can, but if you're concerned about privacy, you shouldn't. When you buy with PayPal there will be a record of you purchasing that coin, so you'll be linked to it. The best ways to buy bitcoin (with other cryptos there might be other factors that help protect your privacy... Monero for instance has built-in privacy features through its ring signatures protocol, so maybe it doesn't matter as much how you got it) are probably to either buy in person from someone and pay with cash (you can use https://localbitcoins.com/ to help you find people selling bitcoin) or to buy from a bitcoin ATM.