Hi ktlynn,
There is! When you go to add a custom image, the WP Media popup will come up where you can pick an image. When you click on the image you want, but before you click “Use Selected Image”, you will see a sidebar come up on the right-hand-side of the screen that gives you all of the image information. There is a line for the ALT tag. Simply fill this out and then select “Use Selected Image”. This alt tag will now be attached to the header image.
If you are using a Featured Image rather than a Custom Image, you will need to go into Media and find the image that will be your featured image and then edit the alt tag there.
Please let me know if this explanation is not clear enough, of if I can help out in any other way.
Thanks,
Nick