How to make a simple rounded button in Storyboard?

Short Answer: YES

You can absolutely make a simple rounded button without the need of an additional background image or writing any code for the same. Just follow the screenshot given below, to set the runtime attributes for the button, to get the desired result.

It won't show in the Storyboard but it will work fine when you run the project.

Note:
The 'Key Path' layer.cornerRadius and value is 5. The value needs to be changed according to the height and width of the button. The formula for it is the height of button * 0.50. So play around the value to see the expected rounded button in the simulator or on the physical device. This procedure will look tedious when you have more than one button to be rounded in the storyboard.

You can do something like this:

@IBDesignable class MyButton: UIButton
{
    override func layoutSubviews() {
        super.layoutSubviews()

        updateCornerRadius()
    }

    @IBInspectable var rounded: Bool = false {
        didSet {
            updateCornerRadius()
        }
    }

    func updateCornerRadius() {
        layer.cornerRadius = rounded ? frame.size.height / 2 : 0
    }
}

Set class to MyButton in Identity Inspector and in IB you will have rounded property:

To do it in the storyboard, you need to use an image for the button.

Alternatively you can do it in code:

 btn.layer.cornerRadius = 10
 btn.clipsToBounds = true