How install facebook on iPhone 4

Check the system requirements for the app. I suspect you will find almost no apps on the App Store still support iOS7 on the iPhone 4 (I have a 4S with iOS9 and it is hard to find apps) and your only recourse is to buy a newer phone.

Facebook requires iOS 9 or higher. You can't run that version on iPhone 4, so if you want Facebook on your phone, it's time for a newer iPhone.