Just thinking your question through for fun. I'm sure there are more dedicated fans who will tear this to shreds:

Tatooine is/was home to numerous moisture farms, which implies at least some moisture in the air to be able to extract. Granted, the size of water droplets needed for a visible rainbow is more than the minimum 1.5% relative humidity needed for those extractors to work. I can't find anything on average relative humidity for Tatooine, but considering 1.5% produces only 1.5L of water/extractor/day, yet the Lars farm supposedly had a moderately successful hydroponics garden, plus drinking, cooking, and minimal cleaning water implies a higher average humidity than 1.5% while still at least scraping by. According to 'The Complete Location Factbook' Tatooine has 1% surface water. To keep surface water in the desert, you need either a ground source (underground water may or may not exist - I found conflicting info), or you need rain. In Star Wars: Rise of the Jedi, when Rey goes to Tatooine, you can see cumulus clouds which also implies occasional rainfall.

So I'd venture that at just the right time, it could be possible to have visible rainbows.

Can other things like fine sand refract rainbows?