Thus, only with javascript.
The correct method is to use a button of the type <input type="submit">, one <button type="submit"> or a <input type="image">, the latter two have a similar effect to button allows other nested elements (including images), and the second allows sending by clicking on a specific image (sending together the coordinates clicked).
If you still want one <a>, follows the code. I do not recommend it because it affects the accessibility of the form.
<form method="post" action="" id="mail_form">
    <div id="newsletter"> 
        <input type="text" name="email_newsletter" />
        <div class="newslink">
            <input type="hidden" name="submit_newsletter" />
            <a href="#" onClick="document.getElementById('mail_form').submit();">ENVIAR</a>
        </div>
    </div>
</form>
Remember that nowadays, using CSS, you can leave the submit with the appearance of a common link, with the advantage of not "breaking" the normal functionality of form.
I’d still have a gambit that’s using a <label for="botaodeenvio"> and hide the original button with position, opacity, etc, but will remain not a <a>. Better use CSS and conventional methods.
							
							
						 
For this you will have to do in javascript or jquery.. It’s okay for you if I give the answer in javascript?
– Silvio Andorinha
@pc_oc I believe that the code that Bacco put is the best solution to your question..
– Silvio Andorinha