I've had things happen professionally. Fairly specific rumor so I can't post it, but a principal still invited me into the office and asked me if it was true -- while we both knew it was nuts.
Doesn't matter what it is. People can believe it. It's mob mentally. Doesn't have to make sense or be rational.
You can't completely ignore it. It lives on its own. Perception is reality. That idea. If a lot of people believe it, the idea becomes true enough.
But you don't want to make a point of denying it. That can make it appear even more true. And you start spreading the rumor yourself that way.
What I would do -- If asked, laugh it off and explain it reasonably. Or possibly even give something that's a bit false/made up, but in your favor. In the jump rope story I glanced at above, if someone asked, you might say something like, "Yeah, I heard about that. Talk about how things get twisted around. Ever hear of the telephone game? The truth is that kid had the jump rope. And, he was the one spinning the rope around. We were just standing nearby. I don't know how that grew out of proportion. I even heard people saying I was whipping him with a rope. Some people..." Leaving out any indication if you were getting bullied by the kid since it could make you look bad.
If it's a professional job setting I'd email my supervisor so it's in writing and then actually talk to them about it.
Also keep in mind -- People are stupid, including those who can influence you, your job, your situation. One influential thing is the first impression or getting them the information first in this case. If they hear the rumor, that becomes somewhat true even if they know if it's false. If they've heard it already, then you're coming along trying to reshape their incorrect idea. If you present them with the information first, that's their first impression and what they'll compare the rumor to. So the key point is to "strike first" and get them the info first. I'm thinking more professional environment and a supervisor for this.
If it's a jump rope situation, it might not be that big of a deal really. If you want to influence your friends, you could say something like, "X happened in the past. But you know what? I actually heard people saying Y happened. Can you believe that? It's like a giant telephone game..." You give them your info first, then present the false info as false. Then kind of laugh it off. If they're your friends, they're going to believe you anyway. If they're not, you'll be a neutral figure and have given them some reasonable explanation for the rumor. If they're already biased against you, it doesn't matter what you do.
Topic: How to deal with false rumors?