Does USCF have a minimum age for tournament directors?
I don’t believe so. There was a list posted a few years ago on this topic with the youngest TD in each category. Made me feel old, I can tell you.
Alex Relyea
There are no age limits on TDs.
It’s five more than the minimum I.Q.
My son became a senior TD at age 18. That is not the youngest by far. He just turned 19
It’s important to have young TDs working their way up the ladder. Many of the most experienced directors are over 50, so it’s nice to see some fresh blood.
What is the age of the youngest at each level? I saw in another post Allen mentioned his son became a senior TD at 18. Do we have an ANTD or NTD who is under 21? I think being of legal drinking age is a requirement, especially at big scholastics. 
I think we’ll all defer to your long experience in this!
Without mentioning individuals (because of privacy reasons), there are two club TDs who are 9 years old, the youngest local TD is 14, the youngest Senior TD is 16, the youngest ANTD is 29 and the youngest NTD is 25.
9 year old club directors! Dang I can play in their tournaments and get paired against other 9 year olds! That’s actually kind of cool. I presume they are directing tournaments at their schools. It’s great to see kids get involved with the directing end. I think it gives them a greater appreciation of the work that goes into putting on a tournament. Also it makes them more aware of the rules when they’re playing. I’ve always been fond of saying that chess players should have to take a test to become a certified tournament player. Though some players are probably already certifiable.
It doesn’t have to be school-related tournaments, Polly. My older son was helping me direct tournaments on Sunday afternoons at the age of 11.
Most under 12 year old directors are just TD assistants, usually at tournaments organized by their parent or coach. They mark up results and handle illegal moves in scholastic sections. Most would defer to an adult to make a ruling that requires any degree of thought. Still, it is nice to see the kids get involved.
The youngest adult tournament organizer that I’ve seen was 12 years old. He did most of the work himself, from advertisement to answering emails to registration and pairings to paying out the prizes. The tournaments attracted about 40-50 players and paid out about $600-750. He did make sure to have one or two more experienced TDs around to help out in a sticky situation (e.g. irate parent of a player).
Michael Aigner
I believe the youngest local TD is now 11 years old. I know his Dad made him work his rear-end off to get it too.
I think I might be the youngest ANTD, IA, IO with both a USCF and a FIDE players rating. I turned 64 last June. 
Frank K. Berry
You may be the ONLY person with all of those distinctions, Frank!