Online Free FavIcon Generator / Image Editor and wordpress
is a good favicon generator.

To add the favicon to your wordpress, put the icon to your root of wordpress installation. And add the line to your header.php of your child theme:
<link href="/favicon.ico" rel="shortcut icon"></link>

For some service, such as blogger, you don't need to generate the favicon by yourself, you just need to a small enough file, such as smaller than 100K, upload it and favicon will be generated from the file.

You can use the online browser-based image editor such as to create the small file.

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