I recently watched a movie called The Cave. In the movie there's a group of spelunkers that get trapped in the cave with a bunch of blind monsters. towards the end of the movie, we find out that the monsters used to be human, and they were infected with a virus that rapidly evolves them to better survive in the cave. Can such a virus (natural or Man-Made) exist.
Yes And No
As L.Dutch pointed out, retroviruses routinely insert their RNA into the DNA of the host cell. If such a virus were carefully engineered, and targeted germ cells (sperm and eggs), it could introduce some scattershot mutations that could result in much more rapid evolution in the progeny of the people infected by the virus. (And result in a lot more stillbirths/miscarriages as mutations kill more often than they're beneficial.)
In The Cave, what the creatures do is not evolution. They change, as an extant organism, from one form to another. This is impossible. Changing the DNA of a host all at once is impossible, and the changes required for major phenotypic (body structure) change would be lethal to an organism not evolved to handle it (insects with cocoons, etc.)
Even leaving aside the impossibility of non-lethal whole-organism phenotype change, the energy demands would be astronomical. Think of how adolescents eat, but much more dramatically.
So could you introduce a virus into a population which would increase the rate of mutation and thereby increase the "rate" of evolution? Yes. Would it be anything like The Cave? No. The Cave's parasites are magic.
I think it has already happened. Some years ago I read in a scientific magazine that in our DNA were found traces of viral genome which were integrated in it a long time ago.
Keep in mind that the difference between a symbiotic and a parasite organism can be very thin, and if the piece of code inserted by the virus doesn't mess too much with the host but actually brings some advantages it can be integrated.
Take for example a virus which produces a precursor of vitamin C: quite paradoxically an infected organism would get an advantage from the infection.
That what happens already with the bacteria we host in our guts.
However it's not the virus that causes evolution: it just gives an evolutionary advantage that needs to be used. Being able to breathe underwater gives no advantage to an animal living in the Sahara desert.
Evolving is probably not the best word to use here. Evolution is a process involving the way species change over time in order to fit into the environment they live in. A virus can force a population to evolve over generations, but not an individual over their lifetime.
Other than that you may consider reading bout gene therapy:
Gene therapy (also called human gene transfer) is a medical field which focuses on the utilization of the therapeutic delivery of nucleic acids into a patient's cells as a drug to treat disease.
It usually involves using a modified virus to infect some of your cells. Instead of giving you an infection, the virus will deploy some genes that you might be missing so that you can start producing insulin or whatever it is that you need but your body cannot produce on your own.
We already do have such viruses ("transposable elements" or "transposons" is the more correct term). They cause "interspersed repeats" - near identical sequences, copies of themselves, spam essentially, to be deposited throughout the human genome over the generations. If the spam lands in an important gene, a child is removed from the gene pool - perhaps in the first generation, or perhaps in some later selective event. However, every now and then the identical copies of the transposable element get confused when the cell is replicating, and because they are not in crucial gene sequence, they have the potential to realign parts of two different genes in a way that allows a "hybrid" gene product to be formed. So they can help to increase the rate of evolution. Several of the recent reviews are good - you can research further if you like.
Nonetheless, these elements work much like HIV, and drugs to treat HIV can stop them from damaging the eye in a common condition called macular degeneration, which can proceed to blindness. So yes, taking HIV drugs for infections caught by ancient ancestors is now a thing.