how to bind click event in angular js?

Use ngClick and ngMouseOver directives respectively

• ngMouseover
• ngClick

e.g.

<div ng-controller="cnt">
    <button ng-click="showMenu()">Click for menu</button>
    <button ng-mouseover="showMenu()">Hover for menu</button>
</div>

edit:

need to call menu() on the element. Should be able to pass element through like below, though this might need editing as I haven't tested the code.

$scope.showMenu = function(element) {
    element.menu();
}

<div ng-controller="cnt">
    <button ng-click="showMenu($element)">Click for menu</button>
    <button ng-mouseover="showMenu($element)">Hover for menu</button>
</div>

You could bind the controller to the directive to use its api

var app=angular.module("ionicApp",['ionic']);
app.directive('custommenu',function(){    
    return{
        restrict:'A',
        scope:{

        },
        controller: 'cnt',
        link:function(scope,element,attr,ctrl){

            $(element).menu();
            $(element).find('li').click(function(){
              scope.showMenu()

            })
        }
    }
})
app.controller('cnt',function($scope){
 $scope.showMenu=function(){
   alert('im here');
 }
})

  var app=angular.module("ionicApp",['']);
  app.directive('custommenu',function(){    
    return{
        restrict:'A',
        scope:{

        },
        link:function(scope,element,attr){

           element.bind('click', function() {

                       // Write your code here
           });
       }
    }
});

app.controller('cnt', function($scope) {

       $scope.isMenuVisible=false;
       $scope.showMenu = function() {

             $scope.isMenuVisible=true;
       }
  });

Avoid using jquery to bind events within angular js

// Update to show menu on click event of some button

<div ng-controller="cnt">
<button ng-click="showMenu()">Show menu</button> 

Now use the scope variable : isMenuVisible to cotrol visibility of menu as:

<div class="menu" data-ng-if="isMenuVisible">    
</div>

I added a JsFiddle version of the answer at here