I've added social links to the nav in the York family templates, so that same method may work for Wexley as well. It requires a bit of a workaround, but it's possible if you are on a Business plan or better.
Step 1: Copy and paste the stylesheet code below into Settings > Advanced > Code Injection into the HEADER box. (You can check the fontawesome.com website to be sure this is the most recent CDN code to serve up the icons.)
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.7.2/css/all.css" integrity="sha384-fnmOCqbTlWIlj8LyTjo7mOUStjsKC4pOpQbqyi7RrhN7udi9RwhKkMHpvLbHG9Sr" crossorigin="anonymous">
Step 2: In Pages, click the + beside the navigation area you want to use (we used Secondary Navigation in the example above) and under Create New Page choose Link.
For Link Title add the Font Awesome code for the icon from their site. For example, instagram is
<i class="fab fa-instagram"></i>
And for Link you’ll just paste in your social media url and remember to click “Open in New Window,” as it’s best practice to open a new window when linking to another website.
More details with a video on this post.