Responsive imagemap on hosted wordpress

I’m a dev, but not hot on WordPress. I’ve a client with a blog hosted on wordpress.com.

They are an illustrator, and they have an image of things like Facebook and Twitter icons done in their style, which need to be clickable.

If it were hosted on their own server, I see solutions, but how to make those image areas clickable AND responsive, has stumped me.

See bottom of the right hand column on desktop: https://pa2sprocketdotcom.wordpress.com/

Is it do-able, and if so, how?

Cheers
J