There's this that I can find:
https://soundcloud.com/noisey/the-room-theme
There IS a promo score that I imagine is floating around somewhere considering Tommy Wiseau worked it to where he has control of the music so at screenings he would sell soundtrack CDs. A quick note about it from the composer himself before seeking this out:
"The unfortunate thing is that they exported it directly from Avid, which is a film editing system. So, if you listen to the CD, you will notice that the loudness of every cue is actually the way it appears in the movie. They didn't master it. If you want to release a CD, you have to master all the music. So, when these songs come in and out, they sound unbelievably soft and unbelievably loud."