How to make a featured image for your entire site, not just a post?

http://www.therunnersports.com Theme: magazine basic

When people or myself share my facebook via things like facebook it gives you an option to display a thumbnail. It gives you an option to use any image on my main page. And the first option being a sponsored image that most people just use cause it’s the first choice and I’m sure they don’t wanna or don’t know you can change it. I don’t want that image because it’s an image of one of my sponsors. Instead I want my own image to be the only option. Is there a way to do that?