Yes. If a church that I attended had such an office, I would be wondering why.
There are organs in smaller churches that perform some of those kinds of duties. Going by such names as board of elders, ethics committee, ethics subcommittee, etc. It doesn't go snooping on its own accord but if someone reports misconduct then they go see if it's true and if so take action. The RCC is so bloomin' big that it could populate a town with people dedicated to this function. But it would be wise to lose "Inquisition" from its name. That has permanent bad press, and stating in retort that the pure church cannot err doesn't help (because we gotta deal with impure churches here on earth).