ng-click event is not firing on button click?

Your Login function needs to be on a scope. Right now, its essentially a private function:

$scope.Login = function () {
  ...
}

assign function to a scope variable.

var adminModule = angular.module('angApp', []);
//Defining a Angular Controller
adminModule.controller('AdminCtrl', ['$scope', '$http',
    function ($scope, $http) {
        $scope.Login = function (U_Name, U_PWD) {
            debugger;
            //Defining the $http service for login the admin user
            $http({
                method: 'POST',
                url: '/Admin/IsAuthenticate',
                data: { User_Name: U_Name, User_PWD: U_PWD }
            }).success(function (result) {
                if (result == true) {
                    alert('user is valid');
                }
                else {
                    alert('unauthorised access!');
                }
            }).error(function (error) {
                //Showing error message 
                $scope.status = 'Unable to connect' + error.message;
            });
        }
        $scope.Login();
    }]);

Edited:

try to use this html code,but i am not sure.it may be that both ng-init and ng-controller are in same div and ng-controller load first after that ng-init :

<div ng-app="angApp">
  <div class="admin-login" ng-controller="AdminCtrl" >
     <h2>using angularjs</h2>
    <input type="text" id="txtUserAng" placeholder="User Name" ng-model="U_Name" />
    <input type="password" id="txtPWDAng" placeholder="Password" ng-model="U_PWD"  />
    <input type="button" id="login" value="login" ng-click="Login()" />
  </div>
</div>