You will need some custom css for this which you should add to Theme Options -> Custom code

.instagram-link {
    color: #fff;
    opacity: 0.7;
    background: none repeat scroll 0% 0% #3A77BE;
    width: 28px;
    height: 28px;
    text-align: center;
    display: inline-block;
    border-radius: 99%;
    line-height: 28px;
    margin-top: 7px;
    margin-right: 3px;

.instagram-link i.fa {
    color: #FFF;
    text-align: center;
    line-height: 28px;

Second, in your footer widget you'll need to actually add a link to your instagram profile

<a href="#" class="facebook-link"><i class="fa fa-facebook"></i></a>
<a href="#" class="twitter-link"><i class="fa fa-twitter"></i></a>
<a href="#" class="googleplus-link"><i class="fa fa-google-plus"></i></a>
<a href="#" class="pinterest-link"><i class="fa fa-pinterest"></i></a>
<a href="#" class="rss-link"><i class="fa fa-rss"></i></a>

<a href="#" class="instagram-link"><i class="fa fa-instagram"></i></a>