Does the White House Communications Agency accept junior 92A soldiers (specifically specialist) or is it rank specific?

It won't say that they don't accept junior Soldiers but they generally don't accept junior Soldiers. Nominatiolve positions like WHCA and Pentagon are looking for NCOs who are capable of working independently and problem solving on their own, not junior Soldiers who need to be watched and told what to do. Of course, you can be held for up to two years waiting on your clearance for the assignment and could very well be an NCO by the time you get there. If you are pretty exceptional then you should apply. If not, get your skills up to par and apply to something. There are other nominative assignments like JSOC, SOLCE, and Delta Support that you can apply to as well once you are an NCO

Not rank specific.

I didn't see anything rank specific requirements on the website nor the application.

https://www.whitehousecommsagency.mil/How-to-Apply/Army/