Yes you can. All you have to do is use a tool like steemconnect's account creation tool: https://v2.steemconnect.com/accounts/create. In order to use that though, you need to have at least 0.1 STEEM on hand, and 15 SP of your own ready to be delegated out to the new account that will be created, or 3 STEEM on hand to power up into that account.
Then there's blocktrades(blocktrades.us) or quicksteem(https://account.buildteam.io/apps/steem-account). Quicksteem just uses blocktrade's APIs to do the same thing as them but with a different front end. They charge about 4 STEEM last I checked to create an account and it comes with 3 STEEM powered up on it.
There's also AnonSteem(https://anon.steem.network/) Its like blocktrades, but costs 5 STEEM or you can pay in BTC/LTC. I haven't used them so I don't know how well they work.
The tool from steemconnect, or blocktrades are the best way to create a STEEM account without having to give up your personal details. When you register through steemit.com, they too are paying the fees to create an account, but they will only do it in exchange for personal details. If you are willing to pay, you don't have to give those details up.