Yes, you can. You’ll just need to enter your gift recipient's shipping address at checkout and check the box "This order is a gift".
You'll be able to send a digital message to let that person know that a special gift is on the way.
Don’t worry - your invoice won’t be included in the package (except for some international orders, where an invoice is attached for customs). If you want to know more about what gets shipped from where check out this nifty article.