HTML
<span class="btn btn-default btn-file">
Browse <input type="file">
</span>
CSS
.btn-file {
position: relative;
overflow: hidden;
}
.btn-file input[type=file] {
position: absolute;
top: 0;
right: 0;
min-width: 100%;
min-height: 100%;
font-size: 100px;
text-align: right;
filter: alpha(opacity=0);
opacity: 0;
outline: none;
background: white;
cursor: inherit;
display: block;
}
Fuente: http://www.abeautifulsite.net/whipping-file-inputs-into-shape-with-bootstrap-3/