Get a (GUI) 2d-arrow to turn to a specific position in 3d-space (similar to a compass)

Here's how I make an airplane rotate based on the direction of the mouse pointer from the center of the screen. This should be able to be modified to do what you want (use a WorldToScreenPoint to get your point, or just use the direction based on subtracting Vector3s):

screenVec = Vector3(Input.mousePosition.x - Global.sCenter.x, Global.sHeight - Input.mousePosition.y - Global.sCenter.y, 0);

 tarAngle= (Mathf.Atan2(screenVec.y,screenVec.x) * Mathf.Rad2Deg)+90;

 if (tarAngle != 0) transform.RotateAround(transform.position,transform.forward, -tarAngle);

Global.sCenter is the screen center pixel coordinates. I simply find the angle between the mouse pointer and the center of the screen (using Atan2) and then roll the target using RotateAround the z-axis of the transform. You could roll your object around its z-axis using the relative x & y coordinate difference...

If you use a 3D arrow and place it in front of the camera you can use the Transform.LookAt() function to set its facing direction. If you use the camera's up vector is should keep the arrow's up vector the same as the camera's up vector.

void Update()
{
    arrowObject.transform.LookAt( waypoint.transform, cam.transform.up );
}

I projected the distance of my target onto a point roughly the same distance away but in front of my camera, and then found the angle from that projected point's up vector required to make it rotate and point towards the target.

 Vector3 up = targetTransform.up;
 float dist = Vector3.Magnitude(targetTransform.position - camera.position);
 Vector3 over = targetTransform.position - (camera.position + camera.forward * dist);
 float ang = Vector3.Angle(up, over);
 if (over.x < 0)
   this.transform.localRotation = Quaternion.Euler(0, 0, ang);
 else
   this.transform.localRotation = Quaternion.Euler(0, 0, -ang);

Here's a sccript I found online, it allows to to rotate any GUI element around a pivot; I have used it as a player marker myself.

 using UnityEngine;
 
 [ExecuteInEditMode()] 
 public class RotatableGuiItem : MonoBehaviour
 {
     public Texture2D texture = null;
     public float angle = 0;
     public Vector2 size = new Vector2(128, 128);
     
     //this will overwrite the items position
     public AlignmentScreenpoint ScreenpointToAlign = AlignmentScreenpoint.TopLeft;
     public Vector2 relativePosition = new Vector2(0, 0);
     
     Vector2 pos = new Vector2(0, 0);
     
     Rect rect;
     Vector2 pivot;
     
     void Start() 
     {
         UpdateSettings();
     }
     
     public void UpdateSettings()
     {
         Vector2 cornerPos = new Vector2(0, 0);
         
         //overwrite the items position
         switch (ScreenpointToAlign)
         {
         case AlignmentScreenpoint.TopLeft:
             cornerPos =new Vector2(0, 0);
             break;
         case AlignmentScreenpoint.TopMiddle:
             cornerPos =new Vector2(Screen.width/2, 0);
             break;
         case AlignmentScreenpoint.TopRight:
             cornerPos = new Vector2(Screen.width, 0);
             break;
         case AlignmentScreenpoint.LeftMiddle:
             cornerPos = new Vector2(0, Screen.height / 2);
             break;
         case AlignmentScreenpoint.RightMiddle:
             cornerPos = new Vector2(Screen.width, Screen.height / 2);
             break;
         case AlignmentScreenpoint.BottomLeft:
             cornerPos = new Vector2(0, Screen.height);
             break;
         case AlignmentScreenpoint.BottomMiddle:
             cornerPos = new Vector2(Screen.width/2, Screen.height);
             break;
         case AlignmentScreenpoint.BottomRight:
             cornerPos = new Vector2(Screen.width, Screen.height);
             break;
         default:
             break;
         }
         
         pos = cornerPos + relativePosition;
         rect = new Rect(pos.x - size.x * 0.5f, pos.y - size.y * 0.5f, size.x, size.y);
         pivot = new Vector2(rect.xMin + rect.width * 0.5f, rect.yMin + rect.height * 0.5f);
     }
     
     void OnGUI() {
 
         GUI.depth = 1;
 
         if (Application.isEditor)
         {
             UpdateSettings();
         }
         Matrix4x4 matrixBackup = GUI.matrix;
         GUIUtility.RotateAroundPivot(angle, pivot);
         GUI.DrawTexture(rect, texture);
         GUI.matrix = matrixBackup;
     }
     
     public enum AlignmentScreenpoint {
         TopLeft, TopMiddle, TopRight,
         LeftMiddle, RightMiddle,
         BottomLeft, BottomMiddle, BottomRight
     }
 }