JSFiddle - React, Tailwind, and code Playground

HTML

<div id="parent">
  <select>
      <option>what</option>
      <option>the</option>
      <option>hell</option>
  </select>
</div>

CSS

#parent{
    background: url('yourimage') no-repeat; 
   /* the width and the height of your image */
    width: 100px;
    height: 30px;
    overflow: hidden;
}

#parent select{
    -webkit-appearance:none;
    -moz-appearance:none;
    appearance:none;
    background:transparent;
    border:none;
    padding-left:10px;
    width: 120px;
    height:100%;    
}