Would tiny high-speed motions cause an object to effectively travel to the future?
Yep.
The mathematical principles that describe time dilation are well established, and you can use them to calculate the difference between proper time (that observed by the thing moving) and coordinate time (that observed by the thing not moving).
For an object rotating about an origin given its orbital distance $r$ and angular velocity $w$, the proper time $\delta T$ can be calculated like so:
$$ \delta T = \Delta T \sqrt{1-(rw/c)^2} $$
Can we do that to a container with a human being in it?
Not without killing that human being. You'll run into problems with friction, compression, and inertia such that you'll open the container and find your prisoner smeared and crispy.
So then how can we do it without making a mess?
The problem is reliably moving individual atoms around in the first place without destroying the body they comprise.
But let's handwave that concern and imagine you've got some miraculous tech that somehow tractor beams onto every atom in a person's body and shakes them each around in a small circular rotation at near light speed.
Let's keep the diameter of rotation so small that we can minimize concerns about macro-scale effects like friction and compression. Under the assumption that you don't want any of the individual's particles to be displaced any farther than the diameter of a hydrogen atom (53 × 10−12 meters), you'll need incredibly high angular velocity to see any significant time dilation... which sadly means we'll have to either address or handwave concerns about how to deal with the accelerative radiation produced (see also Bremsstrahlung).
Doing some quick calculations, an angular velocity of 50 × 1017 radians per second would result in time dilation such that 100 years would pass on the outside for 47 years as perceived by the time-traveling prisoner. But we can do better than that...
The large hadron collider can accelerate protons at 0.999999990$c$ (over 299,792,455 meters per second). If your future tech can match that velocity for all the atoms in a person's body simultaneously within the tiny rotational diameter of a hydrogen atom to prevent molecular dissolution, as given above, you can expect time dilation such that a year in coordinate time will pass by in less than 74 minutes of proper (subjective) time.
So a bit over an hour in the clink equals a year in coordinate time, and a bit over 5 proper days (124 hours) in the clink would remove your dastardly criminal from all friends and loved ones by 100 years.
Is it feasible?
The large hadron collider is probably our best example of artificially accelerating subatomic particles, and it's 27 kilometers long.
Accelerating particles in tiny (submolecular) loops at such speeds has obviously never been accomplished, and I can't even imagine a mechanism for doing so.
Your impressive magical future technology will need to be capable of the following feats:
- accelerating billions of particles simultaneously (uniformly) without destroying the body they comprise
- accelerating particles with extremely high angular velocity over incredibly small distances (such small distances should prevent negative chemical reactions such as friction heating)
- keeping the subject alive, addressing potential problems with respiration, hydration, and ingestion (would this mean accelerating air, food, and water molecules simultaneously?)
- prolonged continuous operation (presumably on the scale of years in coordinate time)
This seems like it would take an incredible amount of energy over an extremely prolonged period of time (presuming the machine will be running continuously in coordinate time, not the prisoner's proper time).
Some of the concerns might be addressed by delivering the punishment in small "doses" instead of all at once, such that the prisoner won't require food and water for the relatively short proper time experienced, simultaneously reducing the duration (and therefore the power consumption) of the continuous treatment in coordinate time.
However, if you've already assumed that this magical technology exists, there's no reason not to overcome its challenges completely unless such problems make your story more narratively interesting.