No, Elon Musk hasn't built a starfighter (at least, not one that he's told us about). But he did borrow some Star Wars terminology when he announced on Twitter that his SpaceX program is testing a new "X-Wing" fin configuration that could help rockets navigate during reentry from space.
The hypersonic grid fins will go up on the next flight of the Falcon 9. As TechCrunch notes:
The SpaceX reusable rocket program has been progressing with varying results, including an explosion over Texas back in August. While the incident didn't result in any injury or even "near injuries," Musk conceded in a tweet that this was evidence that "[r]ockets are tricky."
These new modifications to the rocket should make atmospheric navigation easier, with each fin operating independently to help control the craft's angle, speed and vector. They also fold up and stow during takeoff, so they don't add any additional drag.
The fins themselves will be similar to those used on the Falcon 9R (video below), but larger.