Draws a curved string on a CALayer with angle, radius and text that you give.

ArcTextLayer.swift

import UIKit

// swift port of stackoverflow answer
// http://stackoverflow.com/a/31301238/2048130

extension CGFloat {
  /** Degrees to Radian **/
  var degrees: CGFloat {
    return self * (180.0 / .pi)
  }

  /** Radians to Degrees **/
  var radians: CGFloat {
    return self / 180.0 * .pi
  }
}

func drawCurvedString(on layer: CALayer, text: NSAttributedString, angle: CGFloat, radius: CGFloat) {
  var radAngle = angle.radians

  let textSize = text.boundingRect(
    with: CGSize(width: .max, height: .max),
    options: [.usesLineFragmentOrigin, .usesFontLeading],
    context: nil)
  .integral
  .size

  let perimeter: CGFloat = 2 * .pi * radius
  let textAngle: CGFloat = textSize.width / perimeter * 2 * .pi

  var textRotation: CGFloat = 0
  var textDirection: CGFloat = 0

  if angle > CGFloat(10).radians, angle < CGFloat(170).radians {
    // bottom string
    textRotation = 0.5 * .pi
    textDirection = -2 * .pi
    radAngle += textAngle / 2
  } else {
    // top string
    textRotation = 1.5 * .pi
    textDirection = 2 * .pi
    radAngle -= textAngle / 2
  }

  for c in 0..<text.length {
    let letter = text.attributedSubstring(from: NSRange(c..<c+1))
    let charSize = letter.boundingRect(
      with: CGSize(width: .max, height: .max),
      options: [.usesLineFragmentOrigin, .usesFontLeading],
      context: nil)
    .integral
    .size

    let letterAngle = (charSize.width / perimeter) * textDirection
    let x = radius * cos(radAngle + (letterAngle / 2))
    let y = radius * sin(radAngle + (letterAngle / 2))

    let singleChar = drawText(
      on: layer,
      text: letter,
      frame: CGRect(
        x: (layer.frame.size.width / 2) - (charSize.width / 2) + x,
        y: (layer.frame.size.height / 2) - (charSize.height / 2) + y,
        width: charSize.width,
        height: charSize.height))
    layer.addSublayer(singleChar)
    singleChar.transform = CATransform3DMakeAffineTransform(CGAffineTransform(rotationAngle: radAngle - textRotation))
    radAngle += letterAngle
  }
}


func drawText(on layer: CALayer, text: NSAttributedString, frame: CGRect) -> CATextLayer {
  let textLayer = CATextLayer()
  textLayer.frame = frame
  textLayer.string = text
  textLayer.alignmentMode = kCAAlignmentCenter
  textLayer.contentsScale = UIScreen.main.scale
  return textLayer
}

let view = UIView(frame: CGRect(x: 0, y: 0, width: 200, height: 200))
drawCurvedString(
  on: view.layer,
  text: NSAttributedString(
    string: "This is a test string",
    attributes: [
      NSForegroundColorAttributeName: UIColor.white,
      NSFontAttributeName: UIFont.systemFont(ofSize: 15)
    ]),
  angle: 0,
  radius: 85)

Thanks for sharing,
I would like to share one maybe bug maybe feature :),
line 34
if angle > CGFloat(10).radians, angle < CGFloat(170).radians {
I think this gonna be always "false"
Instead of angle in degree we should use angle in radians so we can have rotated string in the bottom half