Show a UIPickerView when a button is tapped

If you want to do it from Interface Builder then you can add UIPickerView in your storyBoard and initially hide that UIPickerView and when your button tapped show it.

If you want to do this by coding then you can try this.

Define this as global.

var toolBar = UIToolbar()
var picker  = UIPickerView()

Add below code inside your button tap action. I have added Done button in toolbar to dismiss picker.

Note : I write entire code in button action if you don't want to do that just write all code in viewDidLoad and write only these line in your button action self.view.addSubview(picker) and self.view.addSubview(toolBar)

@IBAction func YOUR_BUTTON__TAP_ACTION(_ sender: UIButton) {
    picker = UIPickerView.init()
    picker.delegate = self
    picker.dataSource = self
    picker.backgroundColor = UIColor.white
    picker.setValue(UIColor.black, forKey: "textColor")
    picker.autoresizingMask = .flexibleWidth
    picker.contentMode = .center
    picker.frame = CGRect.init(x: 0.0, y: UIScreen.main.bounds.size.height - 300, width: UIScreen.main.bounds.size.width, height: 300)
    self.view.addSubview(picker)
            
    toolBar = UIToolbar.init(frame: CGRect.init(x: 0.0, y: UIScreen.main.bounds.size.height - 300, width: UIScreen.main.bounds.size.width, height: 50))
    toolBar.barStyle = .blackTranslucent
    toolBar.items = [UIBarButtonItem.init(title: "Done", style: .done, target: self, action: #selector(onDoneButtonTapped))]
    self.view.addSubview(toolBar)
}

On Done button you can remove toolBar as well as PickerView.

@objc func onDoneButtonTapped() {
    toolBar.removeFromSuperview()
    picker.removeFromSuperview()
}

Delegate methods of UIPickerView

func numberOfComponents(in pickerView: UIPickerView) -> Int {
    return 1
}
    
func pickerView(_ pickerView: UIPickerView, numberOfRowsInComponent component: Int) -> Int {
    return YOUR_DATA_ARRAY.COUNT
}
    
func pickerView(_ pickerView: UIPickerView, titleForRow row: Int, forComponent component: Int) -> String? {
    return YOUR_DATA_ARRAY[row]
}
    
func pickerView(_ pickerView: UIPickerView, didSelectRow row: Int, inComponent component: Int) {
    print(YOUR_DATA_ARRAY[row])
}