Use this hack to reCaptcha. It should be clean and in style Bootstrap.

recaptcha.css

.recaptchatable {
    line-height: inherit;
    border: none !important;
}

.recaptchatable #recaptcha_image {
    margin: auto;
    border: none !important;
}

#recaptcha_logo {
    visibility: hidden;
}

.recaptchatable #recaptcha_response_field {
    margin-top: 10px;
    display: block;
    width: 100%;
    height: 38px;
    padding: 8px 12px;
    font-size: 14px;
    line-height: 1.428571429;
    color: #555555;
    vertical-align: middle;
    background-color: #ffffff;
    border: 1px solid #cccccc;
    border-radius: 4px;
    -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
    box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
    -webkit-transition: border-color ease-in-out 0.15s, box-shadow ease-in-out 0.15s;
    transition: border-color ease-in-out 0.15s, box-shadow ease-in-out 0.15s;
}

.recaptchatable #recaptcha_response_field:focus {
    border-color: rgba(79, 167, 79, 0.80);
    outline: 0;
    -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 8px rgba(79, 167, 79, 0.6);
    box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075), 0 0 8px rgba(79, 167, 79, 0.6);
}

recaptcha.js

$(function(){
    var el = $('#recaptcha_response_field');
    el.removeAttr('style').addClass('required textinput textInput form-control');
    el.parent().parent().removeAttr('style');
});