思路：

1. 获取点击的位置
2. 以点击的位置为中心画圆
3. 添加定时器，定时让圆的半径增长
4. 重绘圆

import UIKit
import CoreGraphics

class CustomButton: UIButton {

    // 波纹半径
    var viewRadius: CGFloat = 0
    // 定时器
    var timer: Timer?
    // 点击位置的 x 坐标
    var circleCenterX: CGFloat = 0
    // 点击位置的 y 坐标
    var circleCenterY: CGFloat = 0
    // 波纹动画的颜色
    var targetAnimColor: UIColor = UIColor(red: 216/255.0, green: 114/255.0, blue: 213/255.0, alpha: 0.8)

    override init(frame: CGRect) {
        super.init(frame: frame)
        self.backgroundColor = UIColor(red: 50/255.0, green: 185/255.0, blue: 170/255.0, alpha: 1.0)
    }
    
    required init?(coder aDecoder: NSCoder) {
        fatalError("init(coder:) has not been implemented")
    }

    // 获取点击位置，初始化定时器
    func startButtonAnimation(_ msenderBtn: UIButton, mevent: UIEvent) {
        // 动画期间禁止交互
        self.isUserInteractionEnabled = false
        let button: UIView = msenderBtn as UIView
        // 时间的触摸位置的集合
        let touchSet: NSSet = mevent.touches(for: button)! as NSSet
        var touchArray:[AnyObject] = touchSet.allObjects as [AnyObject]
        let touch1: UITouch = touchArray[0] as! UITouch
        let point1: CGPoint = touch1.location(in: button)
        self.circleCenterX = point1.x
        self.circleCenterY = point1.y
        // 初始化定时器
        timer = Timer.scheduledTimer(timeInterval: 0.01, target: self, selector: #selector(timeaction), userInfo: nil, repeats: true)
        RunLoop.main.add(timer!, forMode: .commonModes)
    }

    // 定制器事件
    func timeaction() {
        // 半径
        self.viewRadius += 5
        // 重绘
        self.setNeedsDisplay()
        if viewRadius > bounds.size.width * 0.5 {
            viewRadius = 0
            timer?.invalidate()
            // 取消波纹
            self.viewRadius = 0
            self.setNeedsDisplay()
            // 交互恢复
            self.isUserInteractionEnabled = true
        }
    }

    // 重绘波纹
    override func draw(_ rect: CGRect) {
        let ctx: CGContext = UIGraphicsGetCurrentContext()!
        let endangle = Double.pi * 2
        // 绘制圆
        ctx.addArc(center:CGPoint(x: circleCenterX, y: circleCenterY) , radius: viewRadius, startAngle: 0, endAngle: CGFloat(endangle), clockwise: false)
        let stockColor: UIColor = targetAnimColor
        stockColor.setStroke()
        // 填充颜色
        stockColor.setFill()
        ctx.fillPath()
    }
}

效果图：

波纹按钮.gif