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)

This is nice, thanks for sharing.
One thing, the notes next to your 'degrees' and 'radian' computed properties are backwards. The "radians to degrees" is degrees to radians.

Thanks for sharing, i would like to ask how to control the drawing path (shape) with given value like, if given value ia 0 it should draw straight line and if the value is negative it should start to bending string from bottom to top and vice versa?

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