Yes, but there is one catch. You need to have an Xbox Live Gold subscription. That is separate from the WWE Network subscription. Here are the instructions from WWE:
In order to experience WWE Network on the Xbox 360, you must have an Xbox 360 with an Xbox Live Gold subscription, and be a WWE Network subscriber.
To use your Xbox 360 with your WWE Network subscription, download the free WWE app from the Apps Marketplace.
- Go to the Apps menu and browse for WWE.
- Choose and download the WWE app.
If you are a subscriber:
- Sign in to your Xbox Live Profile.
- Press Subscriber Sign In using the A button on the control.
- Sign in to your WWE account.
- Enter your Email Address using the onscreen keyboard to enter your information.
- Press A to select.
- Enter your Password using the onscreen keyboard to enter your information.
- Press A to select.
- Press A to select Continue.
- Once your account has been verified, you will be taken to the home screen and can select the programming from WWE Network that you want to watch.