Well, not very acidic, as far as beverages go. One of the major misconceptions about coffee is (1) that it is particularly acidic, and (2) that this acidity causes abdominal pain. As a result of these misconceptions, a cottage industry has developed around 'low-acid' coffee. Here are the facts.
The average pH of black coffee is about 5. That's the same pH as black tea. Herbal teas containing ingredients like rose hips or hibiscus can be considerably more acidic. Even beer, which is not usually thought of as an acidic beverage, has a typical pH of around 4. Most wine and fruit juice is between 3 and 4, and many sodas, due to liberal additions of phosphoric acid, are even lower—Coke is 2.5! Since pH is a logarithmic scale, a substance that is one point lower in pH actually has ten times the concentration of free hydrogen ions. So beer is actually ten times as acidic as coffee.
If coffee causes you stomach problems, don't blame the acidity—unless you also have problems with tea, beer, and fruit. Which is not to say that coffee never causes abdominal pain, just that acids are not the usual culprit. Caffeine alone often triggers abdominal pain, and it's quite possible that there are other aggravating compounds in coffee.
If you prefer the taste of low-acid coffee, fine, but don't avoid acidic-tasting coffee for medical reasons. You're cutting yourself off from a world of beautiful, complex coffees that feature fruity and floral flavors you will never taste in low-acid coffee.