It has an atomic mass of 35.5 because of the readings obtained when it is put in a mass spectrometer, and how these are used to find the Mr. Chlorine has two main isotopes: Cl-35 and Cl-37. In a given sample, there is 25% Cl-37 and 25% Cl-35. 
The equation used to find the Mr of the element is this: (25*37)+(75*35)/100 
Which is 35.5. 
So it's an average mass of an element and all of its naturally occuring isotopes, so won't always be a whole number.

Chlorine has 2 types of isotopes of atomic weights 37 and 35 , present in nature in the ratio 3:1
So, relative atomic mass of chlorine is (37+35)/4 = 35.5
So it has fractional atomic mass