Make enemy's weapon chase a game object

LookAt

Check out this link.

Or review this script, courtesy of Unity!

     *// This complete script can be attached to a camera to make it 
     // continuously point at another object.
     
     // The target variable shows up as a property in the inspector. 
     // Drag another object onto it to make the camera look at it.*

 using UnityEngine;
 using System.Collections;

   *// Create C# script and name is whatever you want.  Make sure to change the name "ExampleClass" 
   // to whatever the name of your script is if you plan to copy and paste.*

 public class ExampleClass : MonoBehaviour {

     public Transform target;
     
     void Update() {
         // Rotate the camera every frame so it keeps looking at the target 
         transform.LookAt(target);
     }
 }

Put this script on the enemy gun or enemy parent, whichever works best in your game. Then drag the game object (player) into the empty transform variable (called target) in the inspector.