Rotate object on Z axis in 2D environment, with mouse.

Unity2DRotateZ.cs

using UnityEngine;
using System.Collections;

public class Rotate : MonoBehaviour
{
	public GameObject objectToRotate;
	public GameObject rotationOverlay; // optional

	void OnMouseDrag ()
	{
		Vector3 pos = Camera.main.WorldToScreenPoint (objectToRotate.transform.position);
		Vector3 dir = Input.mousePosition - pos;
		float angle = Mathf.Atan2 (dir.y, dir.x) * Mathf.Rad2Deg;

		objectToRotate.transform.rotation = Quaternion.AngleAxis (angle, Vector3.forward);
		rotationOverlay.transform.rotation = objectToRotate.transform.rotation;
	}
}