Is an object moving in a circle at a constant speed accelerating?

yes.

Accelerating objects are objects which are changing their velocity - either the speed (i.e., magnitude of the velocity vector) or the direction. An object undergoing uniform circular motion is moving with a constant speed.

Explanation:

Based on all the information that can be discerned from the
graph provided with the question, it may, for all we know, depict
the gyrations of the New York Stock Exchange during World War II,
or possibility the thickness of the ozone layer in the Earth's atmosphere
over the past 77 years. 

It is almost certainly NOT a graphic representation of velocity, since it is
really tough to graph both speed and direction of a moving object.