Can I add a border to an SKSpriteNode, similar to UIView?

Not natively. Though you can just add a SKShapeNode as child whose path you create with CGPathCreateWithRoundedRect.

The following is a simple, dropin extension for SKSpriteNode that will allow you to draw a border with a given color around your node.

import SpriteKit

extension SKSpriteNode {
    func drawBorder(color: UIColor, width: CGFloat) {
        let shapeNode = SKShapeNode(rect: frame)
        shapeNode.fillColor = .clear
        shapeNode.strokeColor = color
        shapeNode.lineWidth = width
        addChild(shapeNode)
    }
}