The horn relay actuates when the wire (black) to the steering column is connected to ground. Normally, the horn button does that, via a copper roller on the turn signal switch. Yours must be grounding out from something else. You will probably need to remove the steering wheel to see what is wrong. You can get a steering wheel puller fairly cheap. I even made one once. My guess is you need a new turn signal switch because the copper roller tower broke off, but could just be a frayed wire. You never tell us the year & model car.
If a later one (~72+) with key switch in the column, it gets much harder, but you can find a good post with photos here.