bootstrap-recaptcha.css

.input-recaptcha {
	width:172px;
}

bootstrap-recaptcha.html

<script type="text/javascript">
	 var RecaptchaOptions = {
	    theme : 'custom',
	    custom_theme_widget: 'recaptcha_widget'
	 };
</script>

<div id="recaptcha_widget" style="display:none">
	<div class="control-group">
		<label class="control-label">reCAPTCHA</label>
		<div class="controls">
	    	<a id="recaptcha_image" href="#" class="thumbnail"></a>
	    	<div class="recaptcha_only_if_incorrect_sol" style="color:red">Incorrect please try again</div>
		</div>
    </div>

   	<div class="control-group">
   		<label class="recaptcha_only_if_image control-label">Enter the words above:</label>
  		<label class="recaptcha_only_if_audio control-label">Enter the numbers you hear:</label>

  		<div class="controls">
  			<div class="input-append">
  				<input type="text" id="recaptcha_response_field" class="input-recaptcha" name="recaptcha_response_field" />
  				<a class="btn" href="javascript:Recaptcha.reload()"><i class="icon-refresh"></i></a>
  				<a class="btn recaptcha_only_if_image" href="javascript:Recaptcha.switch_type('audio')"><i title="Get an audio CAPTCHA" class="icon-headphones"></i></a>
  				<a class="btn recaptcha_only_if_audio" href="javascript:Recaptcha.switch_type('image')"><i title="Get an image CAPTCHA" class="icon-picture"></i></a>
		    	<a class="btn" href="javascript:Recaptcha.showhelp()"><i class="icon-question-sign"></i></a>
  			</div>
  		</div>
	</div>
</div>

<script type="text/javascript" src="https://www.google.com/recaptcha/api/challenge?k={your-public-key}"></script>

<noscript>
    <iframe src="<?php echo $recaptcha_noscript_url; ?>"
       height="300" width="500" frameborder="0"></iframe><br>
    <textarea name="recaptcha_challenge_field" rows="3" cols="40">
    </textarea>
    <input type="hidden" name="recaptcha_response_field" value="manual_challenge">
</noscript>