How to rotate an object using touch controls

First of all, check the documentation for mobile device input at https://docs.unity3d.com/Manual/MobileInput.html .

Now, there are many ways you can do this, but try using cases, something like this example provided by Unity: https://docs.unity3d.com/ScriptReference/TouchPhase.Ended.html

In the Update method, check that you have at least 1 finger in the screen in the first place with Input.touchCount, then by taking the first finger that is in the touchscreen with Input.GetTouch(0) check its TouchPhase with a switch:

• If the phase is TouchPhase.Began establish the starting position

• If the phase is TouchPhase.Moved check how much the position has changed; if it's more than the starting position, move right, else, if is less than starting position move left.

• Finally if the phase is TouchPhase.Exit just send a Debug.Log message that the finger is no longer in the screen (this one is optional).

After all, modifying your code, you'll get something like this:

 public float rotatespeed = 10f;
 private float _startingPosition;

   
 void Update()
 {
     if (Input.touchCount > 0)
     {
         Touch touch = Input.GetTouch(0);
         switch (touch.phase)
         {
             case TouchPhase.Began:
                 _startingPosition = touch.position.x;
                 break;
             case TouchPhase.Moved:
                 if (startingPosition > touch.position.x)
                 {
                     transform.Rotate(Vector3.back, -turnspeed * Time.deltaTime);
                 }
                 else if (startingPosition < touch.position.x)
                 {
                     transform.Rotate(Vector3.back, rotatespeed * Time.deltaTime);
                 }
                 break;
             case TouchPhase.Ended:
                 Debug.Log("Touch Phase Ended.")
                 break;
             }
         }
     }
 }

That would be the code, assuming that your's already work with keyboard input. Hope that helps!