If this is for storing some kind of setting, you may want to look into using persistent storage like NSUserDefaults. When the picker is changed, save the NSUserDefaults value. Then in your viewDidLoad method you can set the picker view to the row you saved earlier.
For example, use these lines when you detect the picker view pickerView has changed to store the row in the key pickerViewValue. Put this in didSelectRow for pickerView.
let defaults = NSUserDefaults.standardUserDefaults()
defaults.setObject(row, forKey: "pickerViewRow")
Then when you load the view, use this to set the picker to the saved row:
let defaults = NSUserDefaults.standardUserDefaults()
if let pickerViewRow = defaults.stringForKey("pickerViewRow")
{
pickerView.selectRow(pickerViewRow, inComponent: 0, animated: true)
}