As long as you have decent pitch, it shouldn't be too hard. Just listen to square waves at various frequencies until you narrow in on the frequency of your tinnitus.

When you play two square waves that are slightly off, you also hear a really obvious pulse that corresponds to how off they are (1 pulse per second means they're off by exactly 1 hz, and so on.) I don't know what the experience of tinnitus would be, but assuming you can hear the tinnitus and a square wave at a close pitch, it should be fairly easy to isolate the exact frequency with a binary search.