You’re not able to change your account to private. However, you can make some adjustments so you won’t be receiving any message from users you’re not following, for example.
In order to do that, head to the settings which you can find under “Me”. In the section “Privacy”, you’re able to flip the switch “Receive messages from anyone”. If turned off, only users that you follow can send you messages. This way, you can determine the group of persons that is able to approach you.