The atomic radius of an anion is larger than the atomic radius of its uncharged state. This is because of the addition of electrons and the changes in the balance of positive and negative charges within the atom.
The atomic radius of an atom is determined by the number of electrons, electron orbitals and protons it has. When traveling across the periodic table from left to right, the number of electron orbitals remains constant, but the number of electrons and protons are simultaneously increased one at a time. The increased number of positively and negatively charged particles increases the effective nuclear charge of the atom and pulls the particles closer together. This causes the decreasing atomic radii trend seen across the periods in a periodic table.
When an atom becomes a negatively charged anion, it fills its outermost electron orbital with additional electrons. Because the electrons now outnumber the protons, the effective nuclear charge is overcome and the atom expands. Although negatively charged particles in the same period all have the same number of electrons if their electron shells are filled, the protons vary, and the same trend of decreasing atomic radii is seen. Cations, or positively charged particles, exhibit a similar trend of decreasing atomic radii across a period when their outer shells are empty; they lose electrons and have a comparative increase in effective nuclear charge.