He got himself arrested so the police would stop bothering him.

Taken from p. 65 of The Last Jedi Visual Dictionary:

Already known to local authorities, DJ purposely arranges his own arrest for a petty crime. The jail is the only place he can grab some sleep with the assurance that he won't be pestered by the Canto Bight Police Department.

From my interpretation, DJ seemed to be bored before he encountered Finn and crew. He had a very relaxed demeanor, indicating that he wasn't stressed out about where he was at all because, as we find out, he could leave at any time.

I think he was probably captured after breaking in somewhere, possibly stealing something, and was locked up and possibly awaiting further processing. He also quite possibly could have been waiting for particular events to happen (changing of guards, casino slowing down for the night, etc.) before making his escape, and finding Finn and Rose accelerated his plans.

Well DJ is not actually the character's real name, but is an abreviation for the philosophy of what DJ believes in: Don't Join.

The Star Wars The Last Jedi The Visual Dictionary reveals "DJ" aren't his initials but actually stands for "Don't Join." Indeed, his cap bears a tin plate with the motto "don't join" stamped on it.

DJ is a cynical, opportunistic survivor who sees society as imbalanced in favor of the wealthy and holds little regard for the First Order, the Resistance, or the New Republic. "He thinks larger causes are for fools, since society is just a machine looking to turn everyone into a cog," according to the book. http://www.ign.com/articles/2017/12/17/star-wars-the-last-jedi-why-benicio-del-toros-character-is-named-dj

So although this does not explain this potential DJ "set-up" (juxtaposition to "Old Wookiee Prisoner Trick"), it may shed some light on where his mind is.

With the idea of being an anarchist, he may be willing to turn on anyone in order to achieve some goal of wealth-equality. On the other hand, "not joining" is another way to say, "doesn't belong to" and therefor there is an irony in that 'every man for himself' usually does not equivicate a better society, so DJ almost seems like a lost cause at this point...

Obvioiusly though, this is speculative and does not explain to what end DJ is working towards, which would give us a better reason why he was in the cell and if he was in fact waiting for Finn/Rose or any other "criminal" bystander. Perhaps the novelization, which is out in April may shed more light on this. Also there is a Canto Bight Novella, but I have not read it.

DJ has a strange gait, way of talking, and general attitude, so what happens later throws this into question a bit, but I got the very distinct impression that he was thrown in there as a drunk and was sleeping off the alcohol. Finn and Rose being noisy woke him up, so he decided it was time to go.