Can you use something like this DEMO? I think it can be achived by setting your image as a background-image
and defining a border-radius
which is equivalent to the diameter of your circle.
You will also have to make use of media queries as is always the case when building a responsive design.
The following is a sample as shown in the fiddle:
CSS
.circle{
height:150px;
width:150px;
background-image:url("http://cdn.playbuzz.com/cdn/3170bee8-985c-47bc-bbb5-2bcb41e85fe9/d8aa4750-deef-44ac-83a1-f2b5e6ee029a.jpg");
background-size:cover;
background-position:center;
border-radius:150px;
margin:0 auto;
}
HTML
<div class="row">
<div class="col-xs-6">
<div class="circle"></div>
</div>
<div class="col-xs-6"></div>