We study one loop corrections to $N=\frac{1}{2}$ supersymmetric gauge theory. In order to show theory is renormalisable in the standard way, we redefine the gaugino and the auxiliary fields($\lambda, \bar F$) which results to extra terms of the lagrangian. We show these extra terms generated by field redefinitions are necessary for renormalisability of the non-anti-commutative field theories. Finally we prove $N = \frac{1}{2}$ supersymmetric gauge theory is renormalisable up to one loop corrections using standard method of the renormalisation. We prove the disagreement between component formalism and superspace formalism is solved and both result to the gauge invariant effective action.