Don here from Shopify!
How this might be implemented in your theme will depend on which theme you are using. :)
If you are using a Shopify theme (all of the free themes in our store are Shopify-made themes) you can contact us here at Shopify to get some small visual edits like this done for your theme under the Shopify Design Policy. :)
If you have a paid Shopify plan and a free Shopify theme you will qualify for up to 60 minutes of free coding time for small visual edits like this.
Let us know here or via our support site if you are using a Shopify theme and you would like us to look at adding this to your theme.
We would need to have the icon image uploaded to your files section in your admin before being able to add it in this instance.
On the other hand, if you are using a premium, paid non-Shopify theme then you would need to either contact your theme's developers or considering hiring an outside Expert Designer to put this customisation in place.
Check out the info above and let us know how we can help you to proceed from here. :)
All the best!
Hi again there!
Don from Shopify once again!
Thanks for getting back to us here to confirm that.
I will send you out an email shortly to the address we have on file for your store here so we can discuss which customisations would be possible for your theme. :)