With the release of WordPress 4.3 it is now possible to add a favicon or site icon directly from your WordPress Admin panel, without the use of a plugin or special theme.
To add a site icon or favicon to your WordPress site:
1. Log into your WordPress Admin Panel.
2. Navigate to Appearance » Customize and click the Site Identity tab.
From the site identity section you can configure or modify your site title, description, and determine how to display them in your WordPress site’s header. You can additionally upload your favicon or site icon. To do this, click on the Select File button and just upload the image you want to use as site icon or favicon.
For a more detailed tutorial on how to add a Favicon for Site Icon in your WordPress click on the link below for a more detailed set of instruction, which includes to do this is older versions of WordPress.