I was about to write that you would need to buy a Roadie license because CX falls under that. I went to the USA Cycling web page to provide a link for you. On the page where you order the license, it noted that the MTB license included CX.
Then I went deeper into the web site and found this schedule of fees:
Domestic
Rider Licenses
Adult Mountain Bike Only $60
Adult Road/Track/Cyclocross Only $60
Interesting. :hmmm: I think you will need to get a Road/Track/CX license but I'm not sure.