In the majority of US states you can order free-T4 testing online and have the blood drawn at a local blood draw center (see my general overview of the process).
The most commonly-suggested measure of T4 is free T4. See the next section if you want total T4.
I'd suggest ordering from Life Extension because they have the cheapest price I know of ($28), and I've been happy with their service. You can also compare the other 6 free-T4 test providers I've found.
Take a look at my state-specific issues page if you're in AZ, MD, NJ, NY or RI.
Smart-dude Ray Peat disagrees with the common view of what free-T4 testing indicates and suggests total-T4 testing instead. So here are the total-T4 providers I've found: