I would suggest dialing it back a little and divorce yourself from your framework or whatever you are using. To center things horizontally there are 2 approaches.
You have to decide based on whether you want the button to be position: inline, inline-block, or block. For mobile and fingers and all that stuff(2014) - I would suggest inline-block or block. So -
if it's inline block, then you can just treat it like text. Set the parent to text-align center;
If it's block, then you you can use margin-right: auto; margin-left: auto;
but that has other issues. Like all the other thinks near it need to be organized properly so that they don't float all over each other and screw everything up. I would suggest you do it like this: jsfiddle
PS - we don't need to see so much code in your fiddle. It's easier to get to the rout of the problem with only the bare necessities. Good luck.
HTML
<aside class="service">
<header>
<h2 class="">Title of module thing</h2>
</header>
<div class="text-wrapper">
<p>Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua Lorem ipsum dolor sit amet…</p>
<a href="#" class="button button-large"><i class="fa fa-credit-card" style="padding-right:10px;"></i> Learn More</a>
</div> <!-- .text-wrapper -->
</aside> <!-- .service -->
CSS
*, *:before, *:after {
-moz-box-sizing: border-box;
-webkit-box-sizing: border-box;
box-sizing: border-box;
} /* start your projext off right */
.service {
border: 1px solid #2ecc71;
font-family: helvetica;
text-align: center;
}
.service header {
background-color: #2ecc71;
}
.service header h2 {
font-size: 1.3em;
font-weight: 400;
color: white;
/* text-align: center; */ /* the parent should have this - not the element */
/* width: 100%; */ /* this is already default because it is a block element */
margin: 0;
padding: .5em;
}
.service .text-wrapper {
padding: 1em;
}
.service p {
text-align: left;
font-size: .9em;
}
.button {
display: inline-block; /*so it's like... "inline" - and can be centered */
background-color: #2ecc71;
text-decoration: none;
color: white;
text-transform: uppercase;
padding: 1em 2em;
-webkit-border-radius: 5px;
border-radius: 5px;
}