코드처럼 전역 변수로 대입하셨다면 send() 함수 내에서 httpMethod 변수를 참조하는데 문제가 없습니다.

httpMethod를 전역변수로 사용해도되지만,

그보다는 input hidden 을 하나 선언해두고 on click 이벤트마다 input에 설정하거나

attribute를 활용하는 방법을 추천드립니다.

1. input hidden 활용

<input type="hidden" id="httpMethod" value="">
<button class="btn btn-secondary dropdown-toggle" id="method_status" type="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">
	Method
</button>
<ul id="method_type" class="dropdown-menu" role="menu" aria-labelledby="searchType">
<li role="presentation">
  <a class="dropdown-item" href="#" value="GET">GET</a>
</li>
<li role="presentation">
  <a class="dropdown-item" href="#" value="POST">POST</a>
</li>
</ul>


$(function () {

    function send() {
        var httpMethod = $('#httpMethod').val();
    }

    $('#method_type li > a').on('click', function () {
        $('#method_status').text($(this).text());
        var httpMethod = $(this).attr('value');
        console.log('선택된 메소드: ' + httpMethod);

        $('#httpMethod').val(httpMethod);
    });    
});

2. attribute or data 활용

<button class="btn btn-secondary dropdown-toggle" id="method_status" type="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false" data-method="">
	Method
</button>
<ul id="method_type" class="dropdown-menu" role="menu" aria-labelledby="searchType">
<li role="presentation">
  <a class="dropdown-item" href="#" value="GET">GET</a>
</li>
<li role="presentation">
  <a class="dropdown-item" href="#" value="POST">POST</a>
</li>
</ul>


$(function () {

    function send() {
        var httpMethod = $('#method_status').attr('data-method');
        // or 
        // var httpMethod = $('#method_status').data('method');
    }

    $('#method_type li > a').on('click', function () {
        $('#method_status').text($(this).text());
        var httpMethod = $(this).attr('value');
        console.log('선택된 메소드: ' + httpMethod);

        $('#method_status').attr('data-method', httpMethod);
        // or 
        // $('#method_status').data('method', httpMethod);
    });    
});

답변주신 모든분들 정말 감사드립니다!