append option to select menu?

Something like this:

var option = document.createElement("option");
option.text = "Text";
option.value = "myvalue";
var select = document.getElementById("id-to-my-select-box");
select.appendChild(option);

$(document).ready(function(){

    $('#mySelect').append("<option>BMW</option>")

})

HTML

<select id="mySelect">
    <option value="volvo">Volvo</option>
    <option value="saab">Saab</option>
    <option value="mercedes">Mercedes</option>
    <option value="audi">Audi</option>
</select>

JavaScript

 var mySelect = document.getElementById('mySelect'),
    newOption = document.createElement('option');

newOption.value = 'bmw';

// Not all browsers support textContent (W3C-compliant)
// When available, textContent is faster (see http://stackoverflow.com/a/1359822/139010)
if (typeof newOption.textContent === 'undefined')
{
    newOption.innerText = 'BMW';
}
else
{
    newOption.textContent = 'BMW';
}

mySelect.appendChild(newOption);

Demo →

You can also use insertAdjacentHTML function:

const select = document.querySelector('select')
const value = 'bmw'
const label = 'BMW'

select.insertAdjacentHTML('beforeend', `
  <option value="${value}">${label}</option>
`)