Square-Cubic Law tells us that at some size the neck of our giant breaks under its own weight(2), but how large is a giant that has a ring that fits a forearm?
Our Giant's finger's diameter is the diameter of the forearm of the human. I am a rather slender person of 2 meters height, my wrist is pretty much skin over bone. To fit my wrist, that'd be $d_{w}=70 \text{ mm}$, while my ring finger is $d_{rf}=22 \text{ mm}$. To slip the ring over the hand (which means I have to deform my hand to the smallest diameter I can achieve) it has to be at least a diameter of $d_{h}=80 \text{ mm}$.
Let's take the 80 mm giant finger, that sounds reasonable, right? So to fit me, the giant has fingers of a diameter that is scaled up by a factor of $f=\frac {d_h}{d_{rf}}=\frac {80}{22}=3.{63}$. Total height would be 7.26 meters or 24 feet, 5.7 inches(1). In either case pretty gigantic... but is that reasonable?
(1) - If the giant wore the ring on the thumb, the factor would be lower, at merely a $\frac{80}{25}=3.2$, so just 6.4 meters/21'.
Reality check time!
Picking out my trusty old matter on the Square-Law, and a BBC documentation we know that humans at 2.5 meters, we have critical health conditions. But if we blow up the bone diameters some, we could go somewhat bigger, but also reengineer other parts... Let's skip the heart and muscles and such.
Just from the bones alone, James Kakalios does offer the basics for an answer in his book The Physics of Superheroes, using Giant Man as an example in chapter 10. Does Size Matter? - The Cube-Square Law.
If Giant-Man is going to maintain a constant density as he
grows, then his mass must increase at the same rate as does his
volume
And we know, Volume goes by length to the cube. A Giant 3.5 times our height occupies approximately 12.25 times the area and has 42.875 times our volume - and thus weight(2). But why do we want to know the area? Actually, we want to know the cross section of some bones, as we know rather well how well bones hold up stress depending on the cross section:
The compressive strength of an object, such as the femur in your thigh or the vertebrae in your spine, is determined by its cross-sectional area—that
is, the area of one of its faces if it were a rectangular solid.
Suppose at his normal height Dr. Pym is six feet tall and weighs
185 pounds [m_h]. His femur at his normal height can support a weight
of 18,000 pounds while a single vertebra [$m_{s_v}$] can support 800 pounds
So, That's an easy thing to calculate, right? Well yes! Let's assume our giant is Hank Pym. His factor is, as we calculated above, $f=3.63$.
So, $m_g=m_h \text{ lbs}\times f^3=8848\text{ lbs}$ while $m_{{s_v}g}=m_{s_v} \text{ lbs}\times f^2=10541\text{ lbs}$. You see easily: Our human vertebra shape scaled up can still support the weight of our giant! Oh, and our giant has just roundabout 1700 pounds of force as a safety margin: At the force of 119% of the own weight the giant's vertebra snaps, while a human has a safety factor of 432%.
As we see, our Giant is still able to live with just about a human skeleton scaled up, but they have a very fatal weakness of strikes to the head and tripping: falling flat induces forces well above the own body's mass. Slipping on a wet surface and not catching yourself is for humans not usually deadly, but for our 3.6 times scaled giants that would be rather deadly.
The muscles and such surely can be addressed rather easily, making them more heavyset and changing their composition. Even increasing all the muscles by an extra factor could mitigate some problems of the biological side (blood flow etc). But that surprisingly does not change the geometry of fingers a lot: A finger contains only a minimal amount of muscles, most o the force in a finger is generated in the lower arm and transmitted via ligaments.
(2) - Note that I speak about weight not mass: Weight is a force, which is on earth linearly related to the mass of an objects: $\vec F=m\vec g$ has a static factor $g=9.81\frac{\text m}{\text s ^2}$ directed towards the center of the planet, so for simplicity's sake, it boils down to this: An object's Weight is the Force created by its Mass times 10, directed to the center of the planet.
This allows us to speak of Weight in terms of Kilograms while it should technically be noted in Newtons - the conversion factor $g=9.81$ (or the rounded $g=10$) is easy enough to keep on the sidelines though, as it rarely matters in a planetary environment.
Vulnerability
As to the vulnerability to head injuries and tripping, if the giant had much thicker cranial bones and was much stockier/more robust (while still being recognisably human in proportion), would you think this would solve that issue somewhat? Are denser and stronger bones reasonable for such a being? – Arkenstein XII
It's not the skull that is the main problem (A skull 3.6 times our skull might arguably survive the impacts of most small arms fire - it's thicker than hip bones). The true problem is the vertebrae: if one doesn't scale up the diameter of the spine by an additional factor, the spine (and for the matter, other bones) would shatter under a normal fall, as that easily exceeds the small 120% of force it is made to keep up against, while humans falling often manage to buffer dangerous falls into their safety range of below 430% of their body weight.(2)
When falling, the body typically impacts with at least two (a stumble) to 10 times the force of its mass (being shoved backwards onto the edge of a pedestrian walkway). To retain the same safety factor our human bones have, the bones need to be not 3.63² times as thick as a humans (normal scaling) but 3.63³ times as thick. This though would flaw our premise of scaleability of the finger bones.
To some degree, it can be mitigated by denser bone material. Typical quotes for human bone range from 1 to 1.9 g/cm³source. Think at least elephant bone density, not human bone density. Some Blainville's Beaked Whale's bones are quoted to be 2.6 g/cm³.
Osteometric parameters show that the relationship of the length of the femur to the circumference is 2.5, 2.75 and 2.8 in elephant, horse and cattle respectively. Similarly, humerus length to circumference is 2.3 in the three species showing isometric scaling. There is a positive allometric scaling be-tween bone weight and bone length; the ratio of femur length to weight is 205 g/cm, 72 g/cm and 64 g/cm in elephants, horses and cattle. The ratio of weight of the humerus to length or weights of the humerus plus femur to their combined length is a good estimate of the body weight in kg= $(\frac{wh}{lh}\times 10)$.here
The rough gist of that paragraph is: The femur bones of elephants are about 3 times as dense per length as those of bovine cattle while having a slightly more slender shape. This means that they are in fact of a more dense design. Note that their notation is kilograms of force(2).
tl;dr: Conclusion
The giants are about 3.2 to 3.6 times as tall as humans (depending on which finger it comes from) and their skeletons are rather similar to humans. Their muscles might be more suited for fast acceleration in contrast to low tiring as humans, which might make them more stocky and heavyset in look, somewhat ogrish. Remember though, that their stride is much larger, so they are still faster than humans, even though they would tire after a shorter time than humans. Their bones might be of a stronger makeup than humans to compensate the lower safety factor the cube-square-law bestows upon them.