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I expected you wouldn't just Google it, but you can get started with the federal bureau of prisons providing raw data: https://www.dropbox.com/s/xwzrnrwp46v34wp/Prison_Data_Shareable.pdf?dl=0
Starting with United States data makes sense as the incarceration rate is so high there. I'll leave the state and international prison searches up to you to follow up on if you decide it's an interesting enough subject. Pew did a summarized study where they lump atheism in with scientology, Satanism, druidism, etc., but it's still a good read.
You might find that there are also correlations between demographics of the incarcerated, uneducated and undereducated, low income, and religious. One certainly isn't necessarily a cause of any other, but it is interesting to find a consistent correlation among all of them.