Rotate Skybox Constantly

How can I rotate the entire skybox Constantly in-game? I don’t want any animated clouds or stuff like that, just rotate the whole skybox. An example would be the Unreal Tournament Map, Facing worlds. I want to accomplish the same thing with my space skybox.
Link to a video with Facing Worlds game-play = - YouTube

Thanks for your help!

The only thing you need to do is add a 6 sided skybox material to you scene, create an empty game object with a script containing the following line:

void Update ()
{
    RenderSettings.skybox.SetFloat("_Rotation", Time.time);
    //To set the speed, just multiply Time.time with whatever amount you want.
}

This will rotate your skybox.

Create a separate camera that only renders the skybox; put it on the furthest back layer, set your other camera(s) to clear “depth only,” and put a script on the skybox camera to rotate it.

This is a shader which can rotate a skybox in any direction without using a second camera. It will rotate with Light0’s rotation. Un-comment the indicated lines if you are using an HDRI map. Cubemaps still work with these lines on, just less efficiently.

Shader "Custom/MovingSkyboxUpload" {
     Properties {
         _CubeMap ("Skybox Cube Map", cube) = "grey" {}
     }
     SubShader {
		 Tags { "Queue"="Background" "RenderType"="Background" "PreviewType"="Skybox" }
		 Cull Off ZWrite Off

         Pass{
         CGPROGRAM
         #pragma vertex vert
         #pragma fragment frag

         //		--------------------	[   un-comment For HDRI Cubemaps   ]	--------------------
		 //#include "UnityCG.cginc"
		 //half4 _CubeMap_HDR;
         //		--------------------	[   un-comment For HDRI Cubemaps   ]	--------------------

         uniform samplerCUBE _CubeMap;
      
         struct vertexInput{
             float4 vertex: POSITION;
         };
         struct vertexOutput{
             float4 pos : SV_POSITION;
             float4 posWorld : TEXCOORD1;
             fixed3x3 R : TEXCOORD4;
         };
      
         vertexOutput vert(vertexInput v){
             vertexOutput o;
             o.pos = mul(UNITY_MATRIX_MVP, v.vertex);
             o.posWorld = mul(unity_ObjectToWorld, v.vertex);
  
             fixed3 new_up = normalize(_WorldSpaceLightPos0.xyz);
 //        folowing code from http://stackoverflow.com/questions/32257338/vertex-position-relative-to-normal
             float3 up = float3(0,1,0);
  
             float3 w = cross(up, new_up);
             float s = length(w);  // Sine of the angle
             float c = dot(up, new_up); // Cosine of the angle
             float3x3 VX = float3x3 (
                 0, -1 * w.z, w.y,
                 w.z, 0, -1 * w.x,
                 -1 * w.y, w.x, 0
             ); // This is the skew-symmetric cross-product matrix of v
             float3x3 I = float3x3 (
                 1, 0, 0,
                 0, 1, 0,
                 0, 0, 1
             ); // The identity matrix
          
             o.R = I + VX + mul(VX , VX) * (1 - c)/(s*s); // The rotation matrix! YAY!
 //        previous code from http://stackoverflow.com/questions/32257338/vertex-position-relative-to-normal
             return o;
         }
      
         float4 frag(vertexOutput i) : COLOR{
             float3 viewDirection = normalize( _WorldSpaceCameraPos.xyz - i.posWorld.xyz );
             viewDirection = mul (viewDirection , i.R);
             //		--------------------	[   un-comment For HDRI Cubemaps   ]	--------------------
             //return fixed4(DecodeHDR (texCUBE(_CubeMap, viewDirection), _CubeMap_HDR),1);
             //		--------------------	[   un-comment For HDRI Cubemaps   ]	--------------------
             return texCUBE(_CubeMap, viewDirection);//		if upside down, add - in front of viewDirection
         }
         ENDCG
     }
 }
 }

Built in Unity 5.4.1

Plus 1 to @ronald677br 's answer. If you want to modify a different skybox, you can also retrieve the skybox component from the camera.
For instance:

public float SkyboxSpeed = 1f;
GetComponent<Skybox>().material.SetFloat("_Rotation", Time.time * SkyboxSpeed);

I found the best way that wasn’t too complex is to add a SkyBox to the “Main Camera” and add a script to it that contains something along the lines of this.

using UnityEngine;

public class HomeCameraRotation : MonoBehaviour {

    public Skybox box;
    public float speed = 5f;

    void Start() {

    }

    void LateUpdate() {
        box.material.SetFloat("_Rotation", Time.time * speed);
    }
}