The "Text Me" button does not work on a computer or tablet. It will only work on your phone. If it doesn't work on your phone, it is because you have not selected a number to use with the "Text Me" button.
See this video for instructions.
Step 1: Log into your vCard Account
Step 2: Choose the vCard you want to edit by clicking on the image
Step 3: Click on the "Contact Info" tab
Step 4: Scroll down to find your phone numbers.
Step 5: Check the box next to "Text Me" for the phone number you want connected to the "Text me" Button.