Listed below are steps required to turn on private browsing in Safari browser on iPhone.
Step 1: Press the menu button on iPhone to access the Home screen.
Step 2: Tap the settings icon on the Home screen.
Step 3: Then tap the Safari option in the Settings screen.
Step 4: Navigate to Privacy section in the Safari Settings and set the value for Private Browsing Switch to ON.
Step 5: Close All Pages popup message will be displayed and if you want to retain the existing open pages then tap the Keep All button otherwise Close All button.
By this way iPhone users can enable private browsing and not to worry about the websites history being stored on iPhone.