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.
I tried with the tone generator linked elsewhere in the thread. One, there's no pulse, which isn't surprising because tinnitus is all in my head. Two, at least for me, tinnitus is not a single well-defined pitch. It fluctuates. Sometimes just by concentrating on it I can move the frequency up and down.
I found a frequency that was pretty close to what I hear (it's convenient that my left ear is mostly normal), and cranked it in my right ear. I now hear something like a distant swarm of bees, or a server room full of very loud fans.
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.