Image as a link in the sidebar can be added in several ways, there are over a thousand extras that resolve this issue. Here we see the data checked and compatible with version 4.7.1.
Adding an image as a link in the sidebar
First you need to install the add-on for the widget in the sidebar on the following link Image Widget.

A simple image widget that uses the native WordPress media manager to add image widgets to your site.
- MU Compatible
- Handles image resizing and alignment
- Link the image
- Title and Description
- Very versatile. All fields are optional.
- Upload, link to external image, or select an image from your media collection using the built in thickbox browser.
- Supports override of template so that you can override the template for your theme!
- Responsive
