Yes, some ants have stingers.
Most ants bite–or in other words they have mandibles (jaws) with which they can grab or pinch objects. However, many ants are too small to effectively bite humans. For example, fire ants first bite, grabbing hold with their mandibles, and then sting repeatedly, injecting venom into their victim. This is why a quick swat at a biting fire ant can often remove them before they sting.
Some very small ants, such as the fire ants’ tiny relatives the thief ants, have stingers too delicate to pierce human skin. On the other hand, some ants like leaf-cutter ants are so well adapted for biting that they no longer have a stinger. - 6legs2many.wordpress.com
These insects belong to the order Hymenoptera, which includes wasps and bees.
Ant communities are headed by a queen or queens, whose function in life is to lay thousands of eggs that will ensure the survival of the colony. Workers (the ants typically seen by humans) are wingless females that never reproduce, but instead forage for food, care for the queen's offspring, work on the nest, protect the community, and perform many other duties. Male ants often have only one role—mating with the queen. After they have performed this function, they may die. - animals.nationalgeographic.com.
Check out this entry from RealScience.com: The Bullet Ant Sting May Be the Worst Pain Known to Man, featuring comedian Hamish Blake's reaction after multiple stings from Amazon bullet ants (watch video below).