Funny, it never occured to me to do that, because it would be, I dunno... cheating? However, after being told that it was just fine to do so I went to the linked sight... and got nowhere. Everything I did landed me back at the FAQ site. There is, as far as I can tell, no way to get a DCI number. Or join the RPGA. (No, going to a game day is not an option.)
1) Go
here
2) Copy the list of bits of information you need to provide to a text editor/Word/somewhere. Fill in the list with the information.
3) On the Customer Service website, click the 'Email Us' tab.
4) Log into your WotC website account, or create one if you do not have one. See my post above if there is a problem here.
5) Select 'RPGA' from the first drop-down menu
6) Select 'Membership request' from the second drop-down menu
7) Ignore the space for your RPGA number
8) Give the email a subject, and write a message asking to be given an RPGA number. Copy the information you've got in your text editor into the email.
9) Click 'Continue'.
10) [I'm working from memory here now] You'll probably get an auto-generated screen trying to provide a solution from the knowledge base rather than sending an email. If so, go to the bottom of the screen and click the button which indicates that you actually want to send an email. I can't recall how it's labelled, but it should be obvious.
11) Turn-around time targets are something like 3 days, though evidence from this thread suggests it is taking considerably less time.
12) Once you receive emails from WotC with your number and password, re-read the earlier part of this thread for directions on how to get fully signed up for the DM Rewards program.
If for some reason this doesn't work, you do not need to go to a game day, as such: if you can find a store which has a supply of DCI cards, if you get one from them you can sign-up on the website with the activation code on the card.
It's not
easy but it it isn't very difficult either. And as the primary role of the RPGA (and DCI) is to track and reward play of WotC games, I think it makes sense that the primary joining method is to be involved with some WotC organised play. This method is a secondary one, but does work, as can be seen in this thread! (Besides, you're getting a free product in exchange for less than 30 minutes work over a couple of days - bargain, I say!)