No, not yet.
However, there are strong indications that they are actively attempting to obtain them. Still, having a nuclear weapon is not like owning an AK-47. Being able to get one, care for it, transport it and ultimately use it carries its own set of challenges. So even if they were able to buy one from, say Pakistan, it would still create difficulties for them to properly use them, not to mention transport them.
Find A Target
Let's assume they want to blow a tactical nuclear weapon in Chicago. What kind of bomb would it be? Most nuclear weapons are larger rockets, so they would have to find a way to transport it close enough and launch it. This would require a complex infrastructure: people to take it there, people to launch it, etc.
The B57 US built tactical nuclear weapon. Other countries built similar ones during the Cold War, and it would be something like this or just the warhead that would have to be acquired and deployed.
Thus, if they were indeed able to acquire such a weapon, chances that they would use it in their neighbourhood in the Middle East where they have somewhat of an infrastructure in place -- Jerusalem or even closer -- are much more likely than Chicago.
A popular movie trope is the nuclear suitcase bombs, and while there is a good chance they do exist (yes, that's actually a debated issue), they're one heck of a large suitcase. The highest-ranking GRU defector Stanislav Lunev claimed that such Russian made devices do exist and many have gone missing. They weight about 50 to 60 pounds and can be remotely controlled. But even if they do exist and are for sale on the Black Markets, they would fetch exorbitant prices and again, require an infrastructure to be transported and used. Inconspicuous they are not. Getting them in and out of countries is not that easy. Also, if they had one, they'd used it a long time ago.
So while there is of course a chance that they are trying to acquire one, as far as we can tell they haven't yet and have difficulties to do so.
Meanwhile, there are weapon systems much easier to get their hands on and equally as dangerous, if not more so.
There are reports that ISIS has used and is attempting to develop and use, chemical weapons, such as mustard gas. Again, this requires an infrastructure and knowledge that isn't that easy to come buy, and reports by intelligence organizations state that what they have produced and used is of small quantities and low quality.
But the chances of them trying to create and use these is larger than that of them acquiring and implementing nuclear weapons.
This is their primary weapon of choice and their most effective one. The ISIS propaganda branch is highly active, and it is through the Internet that they are disseminating their dogmas and extremist believes. Social media outlets such as Facebook, Whatsapp, Twitter, Telegram and others are used to publish their messages, videos, tweets, and articles on their goals and desires.
The recent shooting in California are proof of the success of these weapons. A couple with no known ties to ISIS carried out a violent crime inspired by what they have seen on social media. There was no need for ISIS to buy nukes or mix chemicals. All they had to do was take pictures and tweet.
The pen remains mightier than the sword.