I see that this post is a little out of date but still…
I can show you and everyone else (who is in the same situation as I was this day) how i did it.
First of all, you need html like this:
<div class="circle-avatar" style="background-image:url(http://placekitten.com/g/200/400)"></div>
Than your css class will look like this:
div.circle-avatar{
/* make it responsive */
max-width: 100%;
width:100%;
height:auto;
display:block;
/* div height to be the same as width*/
padding-top:100%;
/* make it a circle */
border-radius:50%;
/* Centering on image`s center*/
background-position-y: center;
background-position-x: center;
background-repeat: no-repeat;
/* it makes the clue thing, takes smaller dimension to fill div */
background-size: cover;
/* it is optional, for making this div centered in parent*/
margin: 0 auto;
top: 0;
left: 0;
right: 0;
bottom: 0;
}
It is responsive circle, centered on original image.
You can change width and height not to autofill its parent if you want.
But keep them equal if you want to have a circle in result.
Link with solution on fiddle
I hope this answer will help struggling people. Bye.