You’re not able to have your feed be private. However, you can make some adjustments to make your account more private in terms of communication.
Only receive messages from friends
Go to the "Privacy" section
Select the option that suits you best:
Everyone can message you
Only creators you follow can message you
No one can message you
Remember that you are in total control of who can message you. If you've started a conversation and want to stop, you can revoke permission to chat: