Can I Trademark a QR Code®?
YES! But only as part of a logo.
QR Codes by themselves are not able to be trademarked since trademark law only covers things that allow the public to easily identify your goods and services, such as names, logos, slogans, sounds, or colors. If you have the ability to see a QR Code and immediately recognize it belongs to say, Flickr, more power to you—but I’d venture that most people could never differentiate one QR Code from another without using it to access the linked site.
However, if you incorporate a QR Code into a logo, you can apply to trademark that logo. Just like any other trademark, you have to be using the logo that includes the QR Code with the branding for your products or services.