public static Vector3 RotateRound(Vector3 position, Vector3 center, Vector3 axis, float angle)
  {
    Vector3 point = Quaternion.AngleAxis(angle, axis) * (position - center);
    Vector3 resultVec3 = center + point;
    return resultVec3;
  }

using UnityEngine;
using System.Collections;
 
public class RotateTest : MonoBehaviour 
{
  public LineRenderer line1;
  public LineRenderer line2;
  public float angle = 30f;
  
  private Vector3 v0;
  private Vector3 v1;
  private Vector3 v2;
  private Vector3 v3;
  private Vector3 v4;
  private Vector3 vCenter;
  void Start()
  {
    v0 = new Vector3(3f,0f,1f);
    v1 = new Vector3(1f, 0f, 3f);
    v2 = new Vector3(4f, 0f, 6f);
    v3 = new Vector3(6f, 0f, 4f);
    vCenter = new Vector3(2f, 0f, 2f);
  }
 
 // Use this for initialization
 void Update () 
  {
   line1.SetVertexCount(5);
    line1.SetPosition(0,v0);
    line1.SetPosition(1,v1);
    line1.SetPosition(2,v2);
    line1.SetPosition(3,v3);
    line1.SetPosition(4,v0);
 
    line2.SetVertexCount(5);
    Vector3 v01 = MathUtils.RotateRound(v0, vCenter, Vector3.up, angle);
    Vector3 v11 = MathUtils.RotateRound(v1, vCenter, Vector3.up, angle);
    Vector3 v21 = MathUtils.RotateRound(v2, vCenter, Vector3.up, angle);
    Vector3 v31 = MathUtils.RotateRound(v3, vCenter, Vector3.up, angle);
    Vector3 v41 = MathUtils.RotateRound(v4, vCenter, Vector3.up, angle);
    line2.SetPosition(0, v01);
    line2.SetPosition(1, v11);
    line2.SetPosition(2, v21);
    line2.SetPosition(3, v31);
    line2.SetPosition(4, v01);
 }
}