How can I find my old mug shot?

IF the photo exists, you will have to check with the jurisdiction where you were arrested.

It is EXTREMELY unlikely they posted mugshots online 20 years ago. It is even LESS likely the when back and posted old mugshots related to cases that never went to trial later.

I have had to do this several times over the years. 20 years ago your photo was taken with either a film camera or a Polaroid, depending on the agency that booked you into jail.

Now, how well they kept their records from that far back matters. Also what matters is the state law regarding how long such records must be kept AND if your mug shot can be released at all. If that time limit has passed, or the state doesn't have mugshots on the list of things you can get, you may have no way at all to get the image. If it has not, and state law allows, it will still be difficult to get the image, as somebody has to dig through several boxes of paper records to find you, your booking number, probably some other ID numbers, and then dig through more boxes to find either the polaroid or the negatives. They can't just look at the photos/negatives, because they have no idea what you look like. They have to find those numbers. Odds are that they have no way to use the negative either. Also, state law may allow the recovery of fees for the processing time it takes to do this, and from personal experience I can tell you this is a day/days long process.

I did this several times for other Police agencies, never for the subject of the photo.

Arrests from 20 years ago in a small town that weren't prosecuted are probably in a cardboard box in a basement somewhere. Internet searches aren't going to help you.

Consider filing a FOIA (Freedom of Information Act) request. You'll need to know how to do this and who to submit it to. Since you have Google, I'll let you take it from here unless you come back with a specific question.

It's an official part of your arrest record. They aren't going to let you have it.