As an Optician I fit Toric contact lenses all the time and yes they have been around for years and are even available in disposable lenses too.
Most Toric contact lenses are weighted (meaning they are thicker on one edge) to prevent the lenses from rotating.
Toric lenses are slightly more complicated to fit as the fit depends not only on the amount of astigmatism, but the shape of the eye too. For example lets say the axis of your cylinder power (astigmatism) is 90 degrees and so the Toric contact lens is ordered so that the weighted edge causes the lens to sit at 90 degrees... well sometimes the shape of the eye can cause the lens to rotate further in one direction... for example 10 degrees.
The lens then has to be ordered with an extra 10 degree compensation so that it sits in the correct place.
It is quite common for a lens to be prescribed using a combination of the sphere and cylindrical power, it is what we call a spherical equivalent and is generally used for milder amounts of astigmatism usually under 1 diopter.
For example if a person has 1 diopter of sphere and 1 diopter of astigmatism, the spherical equivalent is actually 1.5. If you added the full amount of both it would be far too strong and so typically only half of the astigmatism is added to the sphere to determine the contact lens power.
Coming back to the 3D aspect of all this, one has to remember that to see in 3D we must be able to see in a binocular manner, meaning both eyes together as this is how we are able to judge distance and use depth perception. So if one eye is not seeing as clearly, you will have a harder time with 3D glasses too. Of course seeing clearly in general is a factor too