This gist set's all the padding and inset to zero, so that UITextView is ready to wrap the content in it.

UITextField+WrapContent.swift

import UIKit

extension UITextView {
    func wrapToContent() {
        self.contentInset = UIEdgeInsets.zero
        self.scrollIndicatorInsets = UIEdgeInsets.zero
        self.contentOffset = CGPoint.zero
        self.textContainerInset = UIEdgeInsets.zero
        self.textContainer.lineFragmentPadding = 0
    }
}