Centering responsive_slider in header

First of all there’s a problem with your CSS – head is an id and img is a class but your CSS is stating that img is an id and head is a class.

Basically the # denotes an id and the . denotes a class so you’ll need to switch those two around – test and see if it works.

Personally I would do something like…

.slider {
    margin: 0 auto;
    border: 0;
    display: block;
}

And the div would be like…

<div class="slider">
    <?php echo do_shortcode( '[responsive_slider]' ); ?>
</div>

Sometimes you’ll find that margin: 0 auto; doesn’t work so try the left and right margin as auto or try the text-align: center; property and see which works best.

In addition to Zulfikar Nore, the top <header> of TwentyThirteen is 100% width, so center align with margin auto won’t work, because slider expands to full width of its container.

Also, that div might not be necessary. See if this centers the slider, if not use that div and change the class.

.responsive-slider.flexslider {
	max-width: 1080px;
	padding: 0 20px;
	margin: 0 auto 20px; /* adjust top, bottom as needed */
}

On a sidenote, all the changes should be done using Child Theme.
http://codex.wordpress.org/Child_Themes