is 2π a radian?

No, but 2π radians make a complete circle (i.e. is the equivalent of 360°).  One radian is the angle subtended at the centre of the circle by an arc of the circle such that the arc has the same length as the radius of the circle.  One radian is 360/2π degrees:

$${\mathtt{radian}} = {\frac{{\mathtt{360}}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}\right)}} \Rightarrow {\mathtt{radian}} = {\mathtt{57.295\: \!779\: \!513\: \!082\: \!320\: \!9}}$$  degrees

 Note: My "No" refers to the question, not Melody's answer! Melody must have posted while I was writing.

No  $$2\pi$$  is an irrational number.

But

radians can be used to measure angles and $$2\pi$$ radians is equal to 360 degrees.   

does that make sense?