Can you put an apk on an iPhone that isn't jailbroken?

The iOS is 10.2.1 if that helps but I was just curious to see if it's possible.

Added (1). Edit: IPA file not APK sorry.

Added (2). Edit: IPA file not APK sorry.

As I understand it, apk's are only for Android, not iOS, but I don't know what the file extension for iOS applications is.

You could if the.iPA file was purchased by your Apple ID. If not, you would need to use the Apple ID that was used to purchase it…