At this point in Batman: Arkham City, the mayor of Gotham is Quincy Sharp. Sharp was manipulated by Hugo Strange, the current warden of Arkham City, who helped him win the election. In exchange, Sharp basically allowed Strange to do whatever he wanted, helped by a generous amount of mind control. As seen here:
SHARP: Strange came to me back at the asylum. He told me he had
friends, powerful friends. The sort of people who could make things
happen. All I had to do was turn a blind eye to his experiments, and
work on my campaign. He said his friends would ensure that I won.
BATMAN: Who are they?
SHARP: I have no idea. I never met them. They funded everything. Money was no problem. All I had to do was set up Arkham City and put Strange in charge. It made perfect sense. The scum of Gotham needed to be punished. It would be my legacy.
BATMAN: Strange has been removing anyone with evidence against him and sending them into Arkham City. Enjoy your legacy.
Batman: Arkham City
Not only that, Mayor Sharp has declared martial law, as detailed in the Arkham City comic miniseries, which means that all the usual protections against unjustified arrest are irrelevant. In particular, he's given the TYGER guards authorization kill people (and, presumably, to detain them arbitrarily).
This has allowed Strange to imprison, not just Bruce Wayne, but many other political prisoners: anyone with evidence against him, but also anyone who opposed him. For instance, at least one journalist covering Bruce Wayne's press conference was also detained.
So, in short, Hugo Strange didn't have Bruce Wayne arrested, exactly, and the latter certainly didn't commit any crime. He had him detained by his brainwashed private security guards, TYGER security, which he was able to get away with because Mayor Sharp, whose campaign was bankrolled by Strange's backer R'as al Ghul, gave him essentially unlimited leeway due to his belief that Arkham City would help end crime in Gotham, which in turn was influenced by Strange's mind control.