Add image to alert view

Yes, you can add a UIImageView as a subview to your alert view.

var imageView = UIImageView(frame: CGRect(x: 220, y: 10, width: 40, height: 40))
imageView.image = yourImage

alert.view.addSubview(imageView)

Swift 4:

var imageView = UIImageView(frame: CGRect(x: 220, y: 10, width: 40, height: 40))
imageView.image = <#yourImage#>
alert.view.addSubview(imageView)

Here is the solution for Swift 4:

let showAlert = UIAlertController(title: "Demo Alert", message: nil, preferredStyle: .alert)
let imageView = UIImageView(frame: CGRect(x: 10, y: 50, width: 250, height: 230))
imageView.image = image // Your image here...
showAlert.view.addSubview(imageView)
let height = NSLayoutConstraint(item: showAlert.view, attribute: .height, relatedBy: .equal, toItem: nil, attribute: .notAnAttribute, multiplier: 1, constant: 320)
let width = NSLayoutConstraint(item: showAlert.view, attribute: .width, relatedBy: .equal, toItem: nil, attribute: .notAnAttribute, multiplier: 1, constant: 250)
showAlert.view.addConstraint(height)
showAlert.view.addConstraint(width)
showAlert.addAction(UIAlertAction(title: "OK", style: .default, handler: { action in
    // your actions here...    
}))
self.present(showAlert, animated: true, completion: nil)

Output will be somehow like below for all iPhones: