Maybe
The closest thing we have to using ITAR to regulate "software" would be 3D printed gun CAD files. Specifically a company called Defense Distributed makes CAD files for 3D printed guns and the US government used ITAR to stop them from distributing the files online
On Thursday, Defense Distributed founder Cody Wilson received a letter from the State Department Office of Defense Trade Controls Compliance demanding that he take down the online blueprints for the 3D-printable "Liberator" handgun that his group released Monday, along with nine other 3D-printable firearms components hosted on the group's website Defcad.org. The government says it wants to review the files for compliance with arms export control laws known as the International Traffic in Arms Regulations, or ITAR. By uploading the weapons files to the Internet and allowing them to be downloaded abroad, the letter implies Wilson's high-tech gun group may have violated those export controls.
"Until the Department provides Defense Distributed with final [commodity jurisdiction] determinations, Defense Distributed should treat the above technical data as ITAR-controlled," reads the letter, referring to a list of ten CAD files hosted on Defcad that include the 3D-printable gun, silencers, sights and other pieces. "This means that all data should be removed from public acces immediately. Defense Distributed should review the remainder of the data made public on its website to determine whether any other data may be similarly controlled and proceed according to ITAR requirements."
This created a long-running legal battle that saw the Feds give in in 2018
The Justice Department has reached a settlement with the Second Amendment Foundation and Defense Distributed, a collective that organizes, promotes, and distributes technologies to help home gun-makers. Under the agreement, which resolved a suit filed by the two groups in 2015, Americans may "access, discuss, use, reproduce or otherwise benefit from the technical data" that the government had previously ordered Defense Distributed to cease distributing.
The files are (as of 2020) available online again (it's complicated still, but that's outside the scope of Space.SE).
Rockets != Guns
For starters, the Second Amendment doesn't apply to rockets.
Relativity Space uses CAD files to 3D print rocket engines, and they are subject in some regards to ITAR
“We’ve developed our own custom software tools to just streamline those workflows, that really helped,” Ellis said. “Also, just being more of a cloud-enabled company, while still complying with ITAR and security protocols, has been really, really advantageous as well.”
That's the only quote from them regarding ITAR I can find. There's no indication what parts of their rocket are subject to it. So it's possible that the CAD files themselves are not subject to ITAR (Relativity isn't exactly using a printer you can just run out and buy, unlike Defense Distributed). And the design of rocket engines isn't exactly that much of a secret (or the Russians wouldn't have sold us theirs). But we're talking CAD files. The software to launch a rocket is still something you have to get right. I could see ITAR being used to force it to be removed. The question there is would someone be crazy enough to build a rocket using open-source software that isn't flight-proven?
We probably won't know until someone tries
My Magic 8-Ball says "Signs point to no", but there's no on-point precedent. Either way, the US tends to err on the side of "All rockets are subject to ITAR".
