Yes, it is possible! You don't need to beg, you don't need to spend money, you don't need apply for any giveaways. All you need is What.cd
Many private trackers have special invite forums for their PUs and above, but the best i've seen until now is the one What.cd has. They have tons of invites available and it is the best place to go if you are not into F*N, HDBits kinda stuff..

Now i'll tell what you need to do. First of all you need to join to that great music tracker. Luckily they are always open for the interviews.
This mission is not as hard as it seems, just follow the steps below:
1. Go to What.CD: A Beginner's Guide and study for about half an hour.
2. Go to their irc channel and queue for the interview. Here's the link which will be helpful for this step What.CD: A Beginner's Guide
3. Wait for your turn and pass the interview
4. Join the tracker, enjoy music, share and advance to PU

That's it :) You'll gain access to Invites forums as soon as you are a Power User on What.cd. If you ask what kind of invites they offer, i can give some examples and you'll see that totally worth it: PTP, GFT, SCC, BTN, SceneHD, Fux0r, RevTT, PTN, x264, MVids, DB9 and tens of others..

I'd go exactly this way if i wasn't joined to T-I, which I am also thankful for :)
So, Good Luck Everybody and hope the post is helpful for you.

Btw share other cool private tracker invite forums in the comments.
peace