You can copyright an image(digital or print) online and by mail. Images you should consider copyrighting are your website logo, any images you've created that your competition might steal and use, images you use for branding.

How to copyright an image

1. If your image is new, then you will need to submit, by  mail, to the Library of Congress for archival. The image will need to be printed on 8" x 10" acid-free paper and unmounted and mailed in a box.If you are trying to copyright an image that you've already distributed, then you will need to submit the image as defined by the Copyright Office. Circular 7B (Best Edition of Published Copyrighted Works for the Collection of the Library of Congress)
2. Next you will create a digital version of your image under 11.3MB. It's recommended that you create the image in PDF or JPG format.
3. You can upload and register your image by going to the United States Copyright Office's (eCO) or Electronic Copyright Office.
4. There is a fee required to complete registration. The copyright fee can be paid online using credit card or debit card.
5. You will receive the certification of copyright in the mail, about six months, after submitting the image(s).