Why is the radius of anion more than that of the parent atom?

Anion (or negative ion) is formed by the gain of one or more electrons by the gaseous atom. In the anion, nuclear charge is the same as that in parent atom but the number of electrons has increased. As a result, the same nuclear charge acts on relatively larger number of electrons. Thus, effective nuclear charge per electron is decreased which causes the electron cloud to expand. Therefore, anion is always larger than its parent neutral atom.
For example,
Atomic radius of Cl = 99 pm (nuclear charge = - 17 ;e = 17)
Atomic radius of Cl^- = 131 pm (nuclear charge = 17 ; e = 18)