You can do this:

  Vector3 MouseWorldPosition = MainCamera.camera.ScreenToWorldPoint(new Vector3(Input.mousePosition.x, Input.mousePosition.y, 0));
  transform.LookAt(MouseWorldPosition);
  transform.rotation = Quaternion.Euler(new Vector3(0, transform.rotation.eulerAngles.y, 0));

Call this from your player script.

using UnityEngine; using System.Collections;

public class carl : MonoBehaviour { public GameObject ProjectilePrefab; public GameObject MainCamera;
public float PlayerSpeed; public float QuaternionSpeed;

// Update is called once per frame
void Update ()  
{

    Vector3 MouseWorldPosition = MainCamera.camera.ScreenToWorldPoint(new Vector3(Input.mousePosition.x, Input.mousePosition.y, 0));
    transform.LookAt(MouseWorldPosition);
    transform.rotation = Quaternion.Euler(new Vector3(0, transform.rotation.eulerAngles.y, 0));

    // Amout to move
    float inputX = Input.GetAxis("Horizontal") * PlayerSpeed * Time.deltaTime;
    float inputY = Input.GetAxis("Vertical") * PlayerSpeed * Time.deltaTime;


    // Move the Player
    transform.Translate(Vector3.forward * inputX) ;
    transform.Translate(Vector3.left * inputY) ;






    if (Input.GetKey("space"))
    {
            //Fire projectile
            Instantiate(ProjectilePrefab, transform.position,Quaternion.identity);


    }



}

} there it is, he moves, and rotates kinda randomly, but does not rotate to look at mouse postition