Yes, it surely does. The more accurate term for this would be the downregulation of dopamine receptors. It might not be as extreme as, for instance, cocaine addiction, but watching porn does affect the brain. In fact, many drugs hijack the same reward circuits that were evolved for reproduction, that's why they are so addictive:
The human brain is programmed to incentivize behaviors that contribute to survival. The mesolimbic dopaminergic system rewards eating and sexuality with powerful pleasure incentives. Cocaine, opioids, alcohol, and other drugs subvert, or hijack, these pleasure systems, and cause the brain to think a drug high is necessary to survive. [emphasis added] Evidence is now strong that natural rewards such as food and sex affect the reward systems in the same way drugs affect them, thus the current interest in ‘natural addiction.’ ...
Can Pornography Use Become An Actual Brain Addiction? (2011)
You can find numerous evidence that porn does cause the downregulation, but most studies do not isolate porn and instead focus on so called Internet addiction, which I think actually describe the cause of porn usage and not the Internet usage itself for the most part:
An increasing amount of research has suggested that Internet addiction is associated with abnormalities in the dopaminergic brain system. We hypothesized that Internet addiction would be associated with reduced levels of dopaminergic receptor availability in the striatum compared with controls. To test this hypothesis, a radiolabeled ligand [C]raclopride and positron emission tomography was used to assess dopamine D2 receptor binding potential in men with and without Internet addiction. Consistent with our prediction, individuals with Internet addiction showed reduced levels of dopamine D2 receptor availability in subdivisions of the striatum including the bilateral dorsal caudate and right putamen. This finding contributes to the understanding of neurobiological mechanism of Internet addiction.
Reduced striatal dopamine D2 receptors in people with Internet addiction
There are more recent studies that cover porn addiction specifically:
In a recent study by our group, we recruited healthy male participants and associated their self-reported hours spent with pornographic material with their fMRI response to sexual pictures as well as with their brain morphology (Kuhn & Gallinat, 2014). The more hours participants reported consuming pornography, the smaller the BOLD response in left putamen in response to sexual images. Moreover, we found that more hours spent watching pornography was associated with smaller gray matter volume in the striatum, more precisely in the right caudate reaching into the ventral putamen. [emphasis added] We speculate that the brain structural volume deficit may reflect the results of tolerance after desensitization to sexual stimuli.
Neurobiological Basis of Hypersexuality (2016)
And for those who want to know more about porn addiction in general, here's the link to many studies that describe this phenomenon:
There are no scientific studies that say porn is addictive, right?
Anecdote and rant:
I suffered from porn addiction since 12 years old and never knew I was addicted to it until I found Gary Wilson's video on porn addiction and tried to stop. Even though I still experience anxiety, I feel like I start to reconnect to real people. I've become hyper sensitive to sexual stimuli to the point that porn is too stimulating for me and the only option is either to watch it regularly and be numb or never watch it and do something more productive.
P.S. I'm not a native speaker, tried to explain things as accurately as I could.