Can I make #selector refer to a closure in Swift?

Not directly, but some workarounds are possible. Take a look at the following example.

/// Target-Action helper.
final class Action: NSObject {

    private let _action: () -> ()

    init(action: @escaping () -> ()) {
        _action = action
        super.init()
    }

    @objc func action() {
        _action()
    }

}

let action1 = Action { print("action1 triggered") }

let button = UIButton()
button.addTarget(action1, action: #selector(action1.action), forControlEvents: .TouchUpInside)