For better or worse, Apple decided to make it difficult to create email signatures that can contain images with links. Personally, I prefer plain text email signatures – it annoys when I get messages with signature attachments, because I expect message attachments to be related to the message, not a useless signature.
But who cares about what I think!? You don’t want subjective commentary, you want action.
Creating a Rich Text Signature
It’s a strange process to make a rich text signature in Mail.app, but overall it’s quite simple.
Step 1: Create a New Message
The first step involves creating a new email message. Make sure you’re in Rich Text mode. If you’re not, you can change it from the menu.

Step 2: Drag Image to Message
In the New Message window, drag the image(s) that you want in your signature.

Step 3: Select Image and Add Link
After you add the image, click on it to select it, and then add the link via the menu.

Step 4: Select and Paste
Once you’ve finished adding your image(s) and making it linkable, select all (Command + A), and then copy (Command + C). Then go to Signatures in Preferences, and create a new signature. Finally, paste (Command + V) the content, and save the Signature.

It’s convoluted, but it’s by far the easiest way to make a rich text signature in Apple’s Mail app.