How do I get a janitor to clean a prison cell?

As far as I know, there is no way to direct the janitors (or gardeners) where to work; their AI decides what they should do.

There are a few of things you could do to help your prison stay cleaner, each with their own pros and cons.

• You could hire more janitors, which will cost money upfront to hire them, and their ongoing wages.

• You could create some cleaning cupboards and assign prisoners to work there, allowing them to help clean the prison. This can greatly increase your ability to clean your prison. Doing so requires you to have researched prison labour. There is no upfront cost (unless you build a new room for the cupboard), but it will cost a little ongoing expense in the form of bleach that will be auto-purchased for the prisoners to use to clean and the prisoner's $0.50/hour wages. It will also be a source of contraband.

• You could also assign prisoners to work in your laundry, alleviating the janitors need to do this job and allowing them more time to clean. Doing so again requires prison labour. The upside to this option is that there is no upfront cost and the only ongoing expense is the prisoner's $0.50/hour wages. Also, the laundry is not a source of contraband!

Using any one of these things, or better yet a combination of all three should help keep things cleaner.

As DMA mentioned in the comments, working prisoners earn wages but you can recoup some of the wages you pay your prisoners by opening up a shop where they can spend their earnings. This also has other benefits such as giving your prisoners motivation to participate in training programs, it will also improve their concentration in them because they want to earn spending money. The shop itself is not a source of contraband, but the shop goods boxes that are delivered there are. It would be best to make sure your shop goods get carried through a metal detector and by a dog on their way to the shop.