这是一个很好的方法...

func popUpController()
{

    let alertController = UIAlertController(title: "\n\n\n\n\n\n", message: nil, preferredStyle: UIAlertController.Style.actionSheet)

    let margin:CGFloat = 8.0
    let rect = CGRect(x: margin, y: margin, width: alertController.view.bounds.size.width - margin * 4.0, height: 100.0)
    let customView = UITextView(frame: rect)

    customView.backgroundColor = UIColor.clear
    customView.font = UIFont(name: "Helvetica", size: 15)

    //  customView.backgroundColor = UIColor.greenColor()
    alertController.view.addSubview(customView)

    let somethingAction = UIAlertAction(title: "Something", style: UIAlertAction.Style.default, handler: {(alert: UIAlertAction!) in print("something")

        print(customView.text)

    })

    let cancelAction = UIAlertAction(title: "Cancel", style: UIAlertAction.Style.cancel, handler: {(alert: UIAlertAction!) in print("cancel")})

    alertController.addAction(somethingAction)
    alertController.addAction(cancelAction)

    self.present(alertController, animated: true, completion:{})

}

下面的代码适用于UIAlertController的多行UITextView，用Swift 4编写

let alert = UIAlertController(title: "Enter your summary", message: "\n\n\n\n\n\n\n\n", preferredStyle: .alert)
    alert.view.autoresizesSubviews = true

    let textView = UITextView(frame: CGRect.zero)
    textView.translatesAutoresizingMaskIntoConstraints = false

    let leadConstraint = NSLayoutConstraint(item: alert.view, attribute: .leading, relatedBy: .equal, toItem: textView, attribute: .leading, multiplier: 1.0, constant: -8.0)
    let trailConstraint = NSLayoutConstraint(item: alert.view, attribute: .trailing, relatedBy: .equal, toItem: textView, attribute: .trailing, multiplier: 1.0, constant: 8.0)

    let topConstraint = NSLayoutConstraint(item: alert.view, attribute: .top, relatedBy: .equal, toItem: textView, attribute: .top, multiplier: 1.0, constant: -64.0)
    let bottomConstraint = NSLayoutConstraint(item: alert.view, attribute: .bottom, relatedBy: .equal, toItem: textView, attribute: .bottom, multiplier: 1.0, constant: 64.0)
    alert.view.addSubview(textView)
    NSLayoutConstraint.activate([leadConstraint, trailConstraint, topConstraint, bottomConstraint])
    alert.addAction(UIAlertAction(title: "Done", style: .default, handler: { action in
        print("\(String(describing: textView.text))")
    }))
    present(alert, animated: true)

我对Vishal的方法做了一些调整
1.添加了UITextViewDelegate方法，以将初始浅灰色文本显示为占位符，并在textViewDidBeginEditing时将其删除。
1.设置textView的边框宽度、边框颜色和背景颜色，使其可见。

class ViewController: UIViewController, UITextViewDelegate {

...

@IBAction func showAlert(sender: AnyObject) {
    let alertController = UIAlertController(title: "Hello, I'm alert! \n\n\n\n\n\n\n", message: "", preferredStyle: .Alert)

    let rect        = CGRectMake(15, 50, 240, 150.0)
    let textView    = UITextView(frame: rect)

    textView.font               = UIFont(name: "Helvetica", size: 15)
    textView.textColor          = UIColor.lightGrayColor()
    textView.backgroundColor    = UIColor.whiteColor()
    textView.layer.borderColor  = UIColor.lightGrayColor().CGColor
    textView.layer.borderWidth  = 1.0
    textView.text               = "Enter message here"
    textView.delegate           = self

    alertController.view.addSubview(textView)

    let cancel = UIAlertAction(title: "Cancel", style: .Cancel, handler: nil)
    let action = UIAlertAction(title: "Ok", style: .Default, handler: { action in

        let msg = (textView.textColor == UIColor.lightGrayColor()) ? "" : textView.text

        print(msg)

    })
    alertController.addAction(cancel)
    alertController.addAction(action)

    self.presentViewController(alertController, animated: true, completion: {})

}

func textViewDidBeginEditing(textView: UITextView) {
    if textView.textColor == UIColor.lightGrayColor(){
        textView.text = ""
        textView.textColor = UIColor.darkGrayColor()
    }
}
}

您不能在UIAlertController中创建多行textView。您必须为此创建自己的UIAlertController。