Yes, you would probably need to use a URL parameter. The first thing you’re going to need to do is add a custom URL parameter, it needs to be something that won’t conflict with WP. Then output these URLs into the page.
Then you need to get this query argument and alter the post query to short by your custom field either ‘ASC’ or ‘DESC’ depending on what link is clicked. http://www.advancedcustomfields.com/resources/query-posts-custom-fields/
