Cursor rotating around player

In my game, I have my cursor orbit around the player in a circle, instead of being free. This works really well, but I want the cursor to act the same way with a joystick. How can I make this code also work with the joystick?

Here is a link to a GIF showing what I mean: https://imgur.com/kTg7qiI

Code (CSharp):

1. private void Start()
2.     {
3.         target = GameObject.FindGameObjectWithTag("Player").transform;
4.  
5.         Cursor.visible = false;
6.         Cursor.lockState = CursorLockMode.Confined;
7.     }
8.  
9.     private void Update()
10.     {
11.         Vector3 targetScreenPos = Camera.main.WorldToScreenPoint(target.position);
12.         targetScreenPos.z = 0;
13.         Vector3 targetToMouseDir = Input.mousePosition - targetScreenPos;
14.  
15.         Vector3 targetToMe = transform.position - target.position;
16.         targetToMe.z = 0;
17.  
18.         Vector3 newTargetToMe = Vector3.RotateTowards(targetToMe, targetToMouseDir, 3, 0f);
19.  
20.         transform.position = target.position + 3 *newTargetToMe.normalized;
21.     }

 

Seems like a joystick would be easy:

Vector2 joystickVector = Vector2.clampMagnitude(new Vector2(Input.GetAxis("Horizontal"), Input.GetAxis("Vertical")), 1.0f);
Vector2 offset = joystickVector * cursorOffsetDistance;
transform.position = target.position + offset;

Didn't test this, so forgive me for any mistakes but I think the general idea should work.