Similar to the top answer, I used the unicode character in the value= section of the HTML and called FontAwesome as the font family on that input element. The only thing I'll add that the top answer doesn't cover is that because my value element also had text inside it after the icon, changing the font family to FontAwesome made the regular text look bad. The solution was simply to change the CSS to include fallback fonts:
<input type="text" id="datepicker" placeholder="Change Date" value="? Sat Oct 19" readonly="readonly" class="hasDatepicker">
font-family: FontAwesome, Roboto, sans-serif;
This way, FontAwesome will grab the icon, but all non-icon text will have the desired font applied.